FORM OF NON-QUALIFIED STOCK OPTION AWARD AGREEMENT Granted by GOUVERNEUR BANCORP, INC. under the GOUVERNEUR BANCORP, INC. 2025 EQUITY INCENTIVE PLAN

Exhibit 10.4

FORM OF

NON-QUALIFIED STOCK OPTION AWARD AGREEMENT

Granted by

GOUVERNEUR BANCORP, INC.

under the

GOUVERNEUR BANCORP, INC. 2025 EQUITY INCENTIVE PLAN

This Non-Qualified Stock Option Agreement ("Option" or "Agreement") is and will be subject in every respect to the provisions of the Gouverneur Bancorp, Inc. 2025 Equity Incentive Plan (the "Plan"), which are incorporated herein by reference and made a part hereof, subject to the provisions of this Agreement. A copy of the Plan and related prospectus have been provided or made available to each person granted a Stock Option pursuant to the Plan. The holder of this Option (the "Participant") hereby accepts this Option, subject to all the terms and provisions of the Plan and this Agreement, and agrees that all decisions under and interpretations of the Plan and this Agreement by the committee appointed to administer the Plan (the "Committee") or the Board of Directors will be final, binding and conclusive upon the Participant and the Participant's heirs, legal representatives, successors and permitted assigns. Except where the context otherwise requires, the term "Company" means Gouverneur Bancorp, Inc. and its parent and all present and future subsidiaries as defined in Section 424(e) and 424(f) of the Internal Revenue Code of 1986, as amended from time to time (the "Code"). Capitalized terms used herein but not defined will have the same meaning as in the Plan.

1. Name of Participant:

2. Date of Grant:

3. Total number of shares of Company common stock, $0.01 par value per share, which may be acquired pursuant to this Option: ___________ (subject to adjustment pursuant to Section 9 below)

4. Exercise price per share: _________________ (subject to adjustment pursuant to Section 9 below)

5. Expiration Date of Option: _______________. Notwithstanding anything in this Agreement to the contrary, no part of this Option may be exercised at any time on or after the expiration date.

6. Vesting Schedule. Unless sooner vested in accordance with the terms of the Plan and this Agreement, the Option granted hereunder will vest (i.e., become exercisable) in accordance with the following schedule:

Vesting Date Number of Shares Exercisable

7. Exercise Procedure and Delivery of Notice of Exercise of Option. This Option may be exercised in whole or in part by the Participant's delivery to the Company of written notice in a form provided by the Company setting forth the number of shares with respect to which this Option is to be exercised, together with payment by cash or other means acceptable to the Committee, in accordance with the Plan.

8. Delivery of Shares. Delivery of shares of Stock upon the exercise of this Option will comply with all applicable laws (including the requirements of the Securities Act of 1933, as amended) and the applicable requirements of any securities exchange or similar entity.

9. Adjustment Provisions. This Option, including the number of shares subject to the Option and the exercise price, will be adjusted upon the occurrence of the events specified in, and in accordance with the provisions of, Section 3.4 of the Plan.

10. Accelerated Vesting and Exercisability Period. Notwithstanding the vesting schedule set forth in Section 6 of this Agreement, the vesting and exercisability of this Option upon a Termination of Service in certain events will be as follows:

10.1 Death. In the event of the Participant's Termination of Service by reason of death, any unvested portion of this Option will vest and any unexercised portion of the Option may thereafter be exercised by the Participant's legal representative or beneficiaries for the lesser of: (i) a period of one (1) year from the Participant's date of death, or (ii) the remaining unexpired term of the Option.

10.2 Disability. In the event of the Participant's Termination of Service by reason of the Participant's Disability, any unvested portion of this Option will vest and any unexercised portion of the Option may thereafter be exercised by the Participant or the Participant's legal representative for the lesser of: (i) a period of one (1) year following the Termination of Service due to Disability, or (ii) the remaining unexpired term of the Option.

10.3 Termination of Service at or Following a Change in Control. In the event of the Participant's Involuntary Termination of Service at or following a Change in Control, any unvested portion of the Option will vest and any unexercised portion of the Option may be exercised by the Participant or the Participant's legal representative for a period of one (1) year following the Participant's Involuntary Termination of Service.

10.4 Termination for Cause. In the event of the Participant's Termination of Service for Cause, all Options subject to this Agreement that have not been exercised will immediately expire and be forfeited.

10.5 Other Termination. In the event of the Participant's Termination from Service for any reason other than due to death, Disability, Involuntary Termination at or following a Change in Control, or for Cause, this Option may thereafter be exercised, only to the extent it was exercisable at the time of the termination and only for the lesser of: (i) a period of three (3) months following the termination, or (ii) the remaining unexpired term of the Option.

11. Miscellaneous.

11.1 No Option will confer upon the Participant any rights as a stockholder of the Company prior to the date on which the individual fulfills all conditions for receipt of such rights.

11.2 Except as otherwise provided for in the Plan, this Agreement may not be amended or otherwise modified unless evidenced in writing and signed by the Company and the Participant.

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11.3 At the discretion of the Committee, a Non-Qualified Option granted under the Plan may be transferable by the Participant, provided, however, that transfers will be limited to Immediate Family Members of Participants, trusts and partnerships established for the primary benefit of Immediate Family Members or to charitable organizations, and provided, further, that the transfers are not made for consideration to the Participant.

11.4 Except as otherwise required by law, this Option will be subject to any required federal, state and local tax withholding, which may be effected in the manner or manners permitted by the Company.

11.5 The Company is not providing any tax, legal or financial advice, nor is the Company making any recommendations regarding the Participant's participation in the Plan, or the Participant's acquisition or sale of the underlying shares. The Participant is hereby advised to consult with his or her own personal tax, legal and financial advisors regarding the Participant's participation in the Plan before taking any action related to the Plan.

11.6 This Agreement will be governed by and construed in accordance with the laws of the State of New York.

11.7 Nothing in this Agreement will interfere with or limit in any way the right of the Company or any Affiliate to terminate the employment or service of the Participant at any time, nor confer upon the Participant any right to continue in the employ or service of the Company or any Affiliate.

11.8 This Option is subject to forfeiture in accordance with the provisions of Section 7.18 of the Plan or as otherwise adopted by the Company.

11.9 In the event of a conflict between the terms of this Agreement and the Plan, the terms of the Plan will control.

11.10 This Option is subject to all laws, regulations and orders of any governmental authority which may be applicable thereto and, notwithstanding any of the provisions hereof, the Company will not be obligated to issue any shares of stock hereunder if the issuance of such shares would constitute a violation of any such law, regulation or order or any provision thereof.

11.11 This Award Agreement shall be binding upon any successor of the Company, in accordance with the terms of this Agreement and the Plan.

(Signature page follows)

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IN WITNESS WHEREOF, the Company has caused this Agreement to be executed in its name and on its behalf as of the date of grant of this Option set forth above.

GOUVERNEUR BANCORP, INC.

The undersigned hereby accepts the foregoing Option and agrees to the terms and conditions hereof, including the terms and provisions of the Gouverneur Bancorp, Inc. 2025 Equity Incentive Plan. The undersigned hereby acknowledges receipt of a copy of the Gouverneur Bancorp, Inc. 2025 Equity Incentive Plan and related prospectus.

PARTICIPANT

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