Exhibit 4.1

Personal and Confidential

December 1, 2025

Apimeds Pharmaceuticals US, Inc.

Dr. Vin Menon

Chief Executive Officer

100 Matawan Rd, Suite 325

Matawan, New Jersey

Re: Financial Advisory Agreement (this “Agreement”)

Dear Mr. Menon,

E.F. Hutton & Co. LLC (“E.F. Hutton & Co.”) is pleased to act as an exclusive financial advisor for Apimeds Pharmaceuticals US, Inc., (separately or together with its subsidiaries and affiliates referred to herein as the “Company”, and together with E.F. Hutton & Co, the “Parties”). The Company and E.F. Hutton & Co. agree as follows:

1. Description of Services. The Company hereby retains E.F. Hutton & Co. and E.F. Hutton & Co. hereby agrees to provide general financial and placement advisory services to the Company, and E.F. Hutton & Co. accepts such retention on the terms and conditions set forth in this Agreement. E.F. Hutton & Co. will advise the Company and provide any of the services described on the attached Exhibit A (collectively referred to as the “Advisory Services”) and such other area or areas as the Company may subsequently engage E.F. Hutton & Co.

This Agreement constitutes the entire agreement with respect to the subject matter hereof and supersedes all prior engagement letters or financial advisory agreements between the Parties.

2. Compensation. As consideration for the Advisory Services pursuant to this Agreement, E.F. Hutton & Co. shall be entitled to receive, and the Company agrees to pay E.F. Hutton & Co., the following compensation:

(a) The Company shall issue to E.F. Hutton & Co., concurrently with the execution of this Agreement and in consideration for the Advisory Services, a number of shares of the Company’s common stock equal to three percent (3.0%) of the fully diluted shares of the Company (the “Advisor Shares”). The number of Advisor Shares issuable to E.F. Hutton & Co. hereunder is 4,558,044, calculated based on 151,934,832 fully diluted shares of the Company.

(b) The Parties acknowledge that certain cash compensation owed to E.F. Hutton & Co. has been deferred (the “Deferred Compensation”) and agree that the Company shall pay such Deferred Compensation to E.F. Hutton & Co. in good faith as funds become available under the Ayrton facility; for the avoidance of doubt, the outstanding amount of Deferred Compensation owed under this Agreement is Five Hundred Thousand Dollars ($500,000).

(c) The Parties acknowledge and agree that any Bitcoin or other digital-asset infusions by promoters, including Calfin Capital, shall constitute business development or strategic arrangements and shall not be deemed a “Financing” or “Transaction” for purposes of this Agreement, nor shall such infusions be subject to the Financing Fees set forth in Exhibit B.

(d) The Company and E.F. Hutton & Co. acknowledge and agree that, in the course of performing Advisory Services requested by the Company hereunder, E.F. Hutton & Co. may communicate with or introduce the Company to third parties who may be interested in providing financing to the Company (a “Financing”) or, upon request by the Company, in advising or entering into a transaction with the Company, including, without limitation, a merger, acquisition or sale of stock or assets, joint venture, strategic alliance or other similar transaction involving the acquisition by one or more third parties of a majority of the voting securities of the Company or any surviving entity with a third party actually introduced by E.F. Hutton & Co. to the Company during the Engagement Period (any such transaction, a “Transaction”). The Company agrees that if during the term of this Agreement or within twelve (12) months from the effective date of the termination of this Agreement either the Company or any party to whom the Company was introduced by E.F. Hutton & Co., or who was contacted by E.F. Hutton & Co. on behalf of the Company in connection with its Advisory Services for the Company, proposes a Financing or any Transaction involving the Company, then, if any such Financing or Transaction is consummated, the Company shall pay to E.F. Hutton & Co. fees in accordance with the Fee Schedule at the closing or closings of the Financing or Transaction to which it relates.

3. Release and Waiver of Prior Fees and Arrangements. Except as expressly provided herein, any and all fees accrued or otherwise payable under any prior engagement letter or agreement between the Parties, are hereby waived and cancelled, and neither E.F. Hutton & Co. or the Company shall have any further obligation with respect to any such fees. The Parties further waive, release and terminate all prior arrangements, understandings, commitments, or agreements between the Parties, whether written or oral, in each case arising from or relating to any period prior to December 1, 2025.

4. Information. In connection with E.F. Hutton & Co.’s activities hereunder, the Company will furnish E.F. Hutton & Co. with all information regarding the business, operations, properties, financial condition, standard diligence, management and prospects of the business or specific project (all such information so furnished being the “Information”) that Company deems appropriate and will provide E.F. Hutton & Co. with access to the officers, directors, employees, independent accountants and legal counsel that Company deems appropriate. The Company recognizes and confirms that E.F. Hutton & Co.: (i) will use and rely primarily on the Information and on information available from generally recognized public sources in performing the Advisory Services contemplated by this Agreement without having independently verified the same; (ii) does not assume responsibility for the accuracy or completeness of the Information and such other information. Any advice rendered by E.F. Hutton & Co. pursuant to this Agreement may not be disclosed publicly without E.F. Hutton & Co.’s prior written consent.

5. Right of First Refusal. As additional consideration for its Advisory Services hereunder and as an inducement to cause E.F. Hutton & Co. to enter into this Agreement, for a period of twelve (12) months after the date a Transaction or a Financing is completed, to act as sole investment banker, sole book-runner, and/or sole placement agent, at E.F Hutton & Co.’s discretion, for each and every future offering of a similar nature (debt offering or equity offering as the case may be) (each, a “Subject Transaction”) during such twelve-month period, of the Company or any successor to or any current or future subsidiary of the Company, on terms and conditions similar for such Subject Transactions. E.F. Hutton & Co. shall have the right to determine whether or not any other shall have the right to participate in the Subject Transactions and the economic terms of such participation. For the avoidance of any doubt, the Company shall not retain, engage or solicit any additional investment banker, book-runner, financial advisor, underwriter and/or placement agent in a Subject Transaction during such twelve-month period without the express written consent of E.F. Hutton & Co.

6. Tail Financing. E.F. Hutton & Co. shall be entitled to a cash fee in accordance with the Fee Schedule of the gross proceeds received by the Company from the sale of any equity, debt and/or equity derivative instruments to any investor actually introduced by E.F. Hutton & Co. to the Company during the Engagement Period, in connection with any public or private financing or capital raise (each a “Tail Financing”), and such Tail Financing is consummated at any time during the Term or within the twelve (12) month period following the expiration or termination of the Term (the “Tail Period”), provided that such Tail Financing is by a party actually introduced to the Company in an offering in which the Company has direct knowledge of such party’s participation.

7. Independent Contractor. E.F. Hutton & Co.’s relationship with the Company will be that of an independent contractor and nothing in this Agreement will be construed to create an affiliate relationship between the Company and E.F. Hutton & Co. E.F. Hutton & Co. has no authority to act on behalf of or to enter into any contract, incur any liability or make any representation on behalf of the Company. The Company acknowledges and agrees that E.F. Hutton & Co. is not being engaged as, and shall not be deemed to be, an agent or fiduciary of the Company’s directors, members, management, stockholders or creditors or any other person by this Agreement or the retention of E.F. Hutton & Co. hereunder.

8. Confidentiality. During the Term and for twenty-four (24) months thereafter, both Parties agree to treat all data, material and other information exchange between the Parties as confidential. The Parties acknowledge that E.F. Hutton & Co. may need to retain and disclose certain information relayed to it by the Company for the benefit of regulatory supervision or disclosure and may need to share such information with regulators as requested. Except as and to the extent required by law, neither Party will disclose or use, and will direct its representatives not to disclose or use, any information with respect to any data, materials and other information exchanged during the Term of Engagement, without the express consent of the other Party.

9. Term and Termination. The initial term of this Agreement will be for a period of twelve (12) months commencing on the effective date of this Agreement (the “Initial Term”) and thereafter on a month-to-month basis until terminated by either party as detailed herein (collectively with the Initial Term, the “Term”). Either E.F. Hutton & Co. or the Company may terminate this Agreement at any time upon written notice to the other party during the Term. In the event of such termination, excluding a termination for Cause described herein, the Company shall pay and deliver to E.F. Hutton & Co.: (i) all compensation earned through the date of such termination (“Termination Date”) pursuant to any provision of Section 2(a) and 2(b) and (ii) all compensation which may be earned by E.F. Hutton & Co. after the Termination Date pursuant to Section 2(c). All such fees due to E.F. Hutton & Co. pursuant to the immediately preceding sentence shall be paid to E.F. Hutton & Co. on or before the Termination Date (in the event such fees and reimbursements are earned or owed as of the Termination Date). Pursuant to this Agreement, “Cause” shall mean gross negligence, willful misconduct or an uncured material breach of this Agreement by E.F. Hutton & Co. of which the Company has provided E.F. Hutton & Co. with reasonable notice. Notwithstanding anything expressed or implied herein to the contrary: (i) any other agreement entered into between E.F. Hutton & Co. and the Company may only be terminated in accordance with the terms thereof, notwithstanding an actual or purported termination of this Agreement, and (ii) the terms and provisions of Sections 2, 9, 10 (including, but not limited to, the Indemnification Provisions attached to this Agreement and incorporated herein by reference), 10 and 12 shall survive the termination of this Agreement. Notwithstanding anything to the contrary contained herein, E.F. Hutton shall retain the Advisory Warrants following the expiration of the Term.

10. Indemnification. The Company agrees to indemnify E.F. Hutton & Co. in accordance with the indemnification and other provisions attached to this Agreement as Exhibit C (the “Indemnification Provisions”), which provisions are incorporated herein by reference and shall survive the termination or expiration of this Agreement.

11. Amendments and Waivers. This Agreement may be modified, amended or supplemented only by a written instrument duly executed by E.F. Hutton & Co. and the Company. No term or condition or the breach thereof will be deemed waived, unless it is waived in writing and signed by the party against whom the waiver is claimed. Any waiver or breach of any term or condition will not be deemed to be a waiver of any preceding or succeeding breach of the same or any other term or condition. The failure of any party to insist upon strict performance of any term or condition hereunder will not constitute a waiver of such party’s right to demand strict compliance therewith in the future. If any term, provision, covenant or restriction herein is held by a court of competent jurisdiction to be invalid, void or unenforceable or against public policy, the remainder of the terms, provisions and restrictions contained herein shall remain in full force and effect and shall in no way be affected, impaired or invalidated.

12. Notices. All payments, notices, requests, demands and other communications required or permitted hereunder will be in writing and will be delivered personally (which will include delivery by courier or overnight delivery service) or sent by first class mail, postage prepaid, or sent by facsimile transmission to the Parties at their respective address set forth on the signature page below or at such other address as will be given in writing by a party to the other parties. Items delivered personally or by facsimile transmission will be deemed delivered on the date of actual delivery; items sent by first class mail will be deemed delivered three (3) days after mailing.

13. Governing Law; Jurisdiction and Venue Arbitration. This Agreement will be governed by and construed in accordance with the laws of the State of New York, without regard to principles of conflicts of law. Any controversy between the Parties to this Agreement, or arising out of the Agreement, shall be resolved by arbitration before the American Arbitration Association (“AAA”) in New York, New York. The following arbitration agreement should be read in conjunction with these disclosures:

(a) Arbitration is Final and Binding on the Parties;

(b) The Parties are waiving their right to seek remedies in court, including the right to jury trial;

(c) Pre-Arbitration Discovery is generally more limited than and different from court proceeding; and

(d) The Arbitrators’ award is not required to include actual finding or legal reasoning and any party’s right to appeal or to seek modification of rulings by the arbitrators is strictly limited.

14. Arbitration Agreement. Any and all controversies, disputes or claims between E.F. Hutton & Co. and you or your agents, representatives, employees, directors, officers or control persons, arising out of, in connection with, or with respect to (i) any provisions of or the validity of this agreement or any related agreements, (ii) the relationship of the Parties, or (iii) any controversy arising out of your business shall be conducted by the American arbitration association under its commercial arbitration rules. Arbitration must be commenced by service of a written demand for arbitration or a written notice of intention to arbitrate. If you are a party to such arbitration, to the extent permitted by the rules of the applicable arbitration tribunal, the arbitration shall be conducted in New York, New York. The decision and award of the arbitrator(s) shall be conclusive and binding upon the Parties, and any judgement upon any award rendered may be entered in the state or federal courts located in New York, New York, or any other court having jurisdiction thereof, and neither party shall oppose such entry.

15. Limitation of Liability. In no event shall E.F. Hutton & Co., or any of its affiliates, directors, officers, employees and controlling persons (within the meaning of Section 15 of the Securities Act of 1933, as amended, or Section 20 of the Securities Exchange Act of 1934) be liable to the Company for any incidental, indirect, special or consequential damages (i.e., lost profits) arising out of, or in connection with, this Agreement, whether or not such party was advised of the possibility of such damage. The Company further agrees that the liability limit of E.F. Hutton & Co., or any of its affiliates, directors, officers, employees and controlling persons shall in no event be greater than the aggregate dollar amount which the Company paid to E.F. Hutton & Co. during the term of this Agreement.

16. Successors and Assigns. The benefits of this Agreement shall inure to the Parties, their respective successors and assigns and to the indemnified parties hereunder and their respective successors and assigns, and the obligations and liabilities assumed in this Agreement shall be binding upon the Parties and their respective successors and assigns. Neither E.F. Hutton & Co. or the Company shall assign any of its obligations hereunder without the prior written consent of the other party. Notwithstanding the foregoing, on notice to the Company, E.F. Hutton & Co. may assign any right hereunder, or any E.F. Hutton & Co. assignee may further assign any right hereunder, to a E.F. Hutton & Co. or office of supervisory jurisdiction.

17. Counterparts. This Agreement may be executed in multiple copies, each of which will be deemed an original and all of which will constitute a single agreement binding on the Parties.

18. Entire Agreement. This Agreement (together with documents and agreements entered into herewith) constitutes the entire agreement between the Parties with respect to the subject matter hereof and supersedes all prior and contemporaneous agreements and understandings. Each party to this Agreement acknowledges that no representations, inducements, promises or agreements have been made by any party, or anyone acting on behalf of any party, that are not embodied in this Agreement with respect to the subject matter hereof.

19. Representation. By executing this Agreement, Company acknowledges that it understands and agrees that it has been encouraged, and has had the opportunity to, consult with its own attorney in connection with this Agreement.

20. No Third-Party Beneficiaries. This Agreement does not create, and shall not be construed as creating, any rights enforceable by any person or entity not a party hereto, except those entitled to the benefits of the Indemnification Provisions.

21. Disclaimers. The Company agrees that all decisions, acts, actions, or omissions with respect to the Advisory Services contemplated by this Agreement and the other matters contemplated herein shall be the sole responsibility of the Company, and that the performance by E.F. Hutton & Co. of Advisory Services hereunder will in no way expose E.F. Hutton & Co. to any liability for any such decisions, acts, actions or omissions of the Company.

[Signature Page Follows]

IN WITNESS WHEREOF, the Parties have executed this Agreement as of the day and year first above written.

EXHIBIT A

Advisory Services

E.F. Hutton & Co. will from time to time, at the request of the Company, perform one or a combination of Advisory Services, and consult with and provide assistance to the Company in regard to a Financing or Transaction in any of the following areas but not limited to:

EXHIBIT B

Fee Schedule

Capitalized terms used in this Exhibit shall have the meanings assigned to such terms in the Agreement to which this Exhibit is attached.

Financing Fees:

EXHIBIT C

Indemnification Provisions

Capitalized terms used in this Exhibit shall have the meanings assigned to such terms in the Agreement to which this Exhibit is attached.

The Company agrees to indemnify and hold harmless E.F. Hutton & Co. and each of the other Indemnified Parties (as hereinafter defined) from and against any and all losses, claims, damages, obligations, penalties, judgments, awards, liabilities, costs, expenses and disbursements, and any and all actions, suits, proceedings and investigations in respect thereof and any and all legal and other costs, expenses and disbursements in giving testimony or furnishing documents in response to a subpoena or otherwise (including, without limitation, the costs, expenses and disbursements, as and when incurred, of investigating, preparing, pursing or defending any such action, suit, proceeding or investigation (whether or not in connection with litigation in which any Indemnified Party is a party)) (collectively, “Losses”), directly or indirectly, caused by, relating to, based upon, arising out of, or in connection with, E.F. Hutton & Co.’s acting for the Company, including, without limitation, any act or omission by E.F. Hutton & Co. in connection with its acceptance of or the performance or non-performance of its obligations under the Agreement between the Company and E.F. Hutton & Co. to which these indemnification provisions are attached and form a part (the “Agreement”), any breach by the Company of any representation, warranty, covenant or agreement contained in the Agreement (or in any instrument, document or agreement relating thereto, including any Agency Agreement), or the enforcement by E.F. Hutton & Co. of its rights under the Agreement or these indemnification provisions, except to the extent that any such Losses are found in a final judgment by a court of competent jurisdiction (not subject to further appeal) to have resulted primarily and directly from the gross negligence or willful misconduct of the Indemnified Party seeking indemnification hereunder. The Company also agrees that no Indemnified Party shall have any liability (whether direct or indirect, in contract or tort or otherwise) to the Company for or in connection with the engagement of E.F. Hutton & Co. by the Company or for any other reason, except to the extent that any such liability is found in a final judgment by a court of competent jurisdiction (not subject to further appeal) to have resulted primarily and directly from such Indemnified Party’s gross negligence or willful misconduct.

These Indemnification Provisions shall extend to the following persons (collectively, the “Indemnified Parties”): E.F. Hutton & Co., its present and former affiliated entities, managers, members, officers, employees, legal counsel, agents and controlling persons (within the meaning of the federal securities laws), and the officers, directors, partners, stockholders, members, managers, employees, legal counsel, agents and controlling persons of any of them. These indemnification provisions shall be in addition to any liability which the Company may otherwise have to any Indemnified Party.

If any action, suit, proceeding or investigation is commenced, as to which an Indemnified Party proposes to demand indemnification, it shall notify the Company with reasonable promptness; provided, however, that any failure by an Indemnified Party to notify the Company shall not relieve the Company from its obligations hereunder. An Indemnified Party shall have the right to retain counsel of its own choice to represent it, and the fees, expenses and disbursements of such counsel shall be borne by the Company. Any such counsel shall, to the extent consistent with its professional responsibilities, cooperate with the Company and any counsel designated by the Company. The Company shall be liable for any settlement of any claim against any Indemnified Party made with the Company’s written consent. The Company shall not, without the prior written consent of E.F. Hutton & Co., settle or compromise any claim, or permit a default or consent to the entry of any judgment in respect thereof, unless such settlement, compromise or consent (i) includes, as an unconditional term thereof, the giving by the claimant to all of the Indemnified Parties of an unconditional release from all liability in respect of such claim, and (ii) does not contain any factual or legal admission by or with respect to an Indemnified Party or an adverse statement with respect to the character, professionalism, expertise or reputation of any Indemnified Party or any action or inaction of any Indemnified Party.

In order to provide for just and equitable contribution, if a claim for indemnification pursuant to these indemnification provisions is made but it is found in a final judgment by a court of competent jurisdiction (not subject to further appeal) that such indemnification may not be enforced in such case, even though the express provisions hereof provide for indemnification in such case, then the Company shall contribute to the Losses to which any Indemnified Party may be subject (i) in accordance with the relative benefits received by the Company and its stockholders, subsidiaries and affiliates, on the one hand, and the Indemnified Party, on the other hand, and (ii) if (and only if) the allocation provided in clause (i) of this sentence is not permitted by applicable law, in such proportion as to reflect not only the relative benefits, but also the relative fault of the Company, on the one hand, and the Indemnified Party, on the other hand, in connection with the statements, acts or omissions which resulted in such Losses as well as any relevant equitable considerations. No person found liable for a fraudulent misrepresentation shall be entitled to contribution from any person who is not also found liable for fraudulent misrepresentation. The relative benefits received (or anticipated to be received) by the Company and its stockholders, subsidiaries and affiliates shall be deemed to be equal to the aggregate consideration payable or receivable by such parties in connection with the transaction or transactions to which the Agreement relates relative to the amount of fees actually received by E.F. Hutton & Co. in connection with such transaction or transactions. Notwithstanding the foregoing, in no event shall the amount contributed by all Indemnified Parties exceed the amount of fees previously received by E.F. Hutton & Co. pursuant to the Agreement.

Neither termination nor completion of the Agreement shall affect these Indemnification Provisions which shall remain operative and in full force and effect. The Indemnification Provisions shall be binding upon the Company and its successors and assigns and shall inure to the benefit of the Indemnified Parties and their respective successors, assigns, heirs and personal representatives.