EXHIBIT 99.10

AMENDMENT TO THE

VRDP SHARES REMARKETING AGREEMENT

AMENDMENT TO THE VRDP SHARES REMARKETING AGREEMENT dated as of June 22, 2022 (this “Amendment”)

BETWEEN:

(1) BlackRock MuniYield New York Quality Fund, Inc., a closed-end investment company organized as a Maryland corporation, as issuer (the “Fund”); and

(2) TD Securities (USA), LLC, a New York corporation, including its successors and assigns, as remarketing agent (the “Remarketing Agent”) and, to the extent provided herein, in its individual capacity.

WHEREAS:

The Fund issued its Series W-7 Variable Rate Demand Preferred Shares (the “VRDP Shares”) pursuant to the Articles Supplementary Establishing and Fixing the Rights and Preferences of VRDP Shares (the “Articles Supplementary”);

The Fund entered into the VRDP Shares Remarketing Agreement with the Remarketing Agent, dated as of June 16, 2020 (the “VRDP Shares Remarketing Agreement”), relating to the VRDP Shares; and

The Fund has designated a Special Rate Period for the VRDP Shares pursuant to, and in accordance with, the Articles Supplementary. The Special Rate Period will commence on June 22, 2022 and will end on June 21, 2023, unless extended, and all references to “Special Rate Period” in this Amendment shall be to such Special Rate Period; and

In connection with the establishment of the Special Rate Period, the Fund has delivered a Notice of Proposed Special Rate Period, dated June 10, 2022 (the “Notice of Proposed Special Rate Period”), pursuant to, and in accordance with, the Articles Supplementary;

The providing of the Notice of Proposed Special Rate Period constituted a Mandatory Tender Event (the “Mandatory Tender Event”);

The Fund intends to issue a Notice of Special Rate Period in the form attached hereto as Exhibit A (the “Notice of Special Rate Period”) to designate such proposed Special Rate Period as a Special Rate Period; and

The Fund and the Remarketing Agent wish to amend certain provisions of the VRDP Shares Remarketing Agreement in respect of the rights and obligations of the Fund and the Remarketing Agent under the VRDP Shares Remarketing Agreement during the Special Rate Period as set forth herein.

NOW, THEREFORE, in consideration of the respective agreements contained herein, and for good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto agree as follows:

ARTICLE I.

DEFINITIONS

Any capitalized terms used in this Amendment but not defined herein shall have the meanings given to such capitalized terms in the VRDP Shares Remarketing Agreement

ARTICLE II.

MODIFICATIONS TO THE VRDP SHARES REMARKETING AGREEMENT

SECTION 2.01 Definitions.

The first paragraph of Section 1 of the VRDP Shares Remarketing Agreement is hereby deleted in their entirety and replaced with the following:

Capitalized terms used herein that are not otherwise defined shall have the meanings assigned to them in the Statement or the Current Notice of Special Rate Period Statement, as applicable. Any day not referred to herein as a Business Day shall mean a calendar day.

The following definitions are added under Section 1 of the VRDP Shares Remarketing Agreement:

“Current Notice of Special Rate Period” means the Notice of Special Rate Period dated June 22, 2022, as amended from time to time.

“Current Special Rate Period” means the current Special Rate Period for the VRDP Shares designated in accordance with the Statement.

SECTION 2.02 Terms Applicable During the Current Special Rate Period.

The following replaces Section 3 of the VRDP Shares Remarketing Agreement:

Section 3. Terms Applicable During the Current Special Rate Period.

The terms set forth in this Section 3 shall be applicable during, and only during, the Current Special Rate Period and such terms shall supersede any other terms, provisions or obligations set forth in this Agreement during the Current Special Rate Period. This Section 3 shall have no force or effect after the last day of the Current Special Rate Period and shall be deemed deleted and removed from this Agreement in its entirety thereafter without any further action from the Fund or the Remarketing Agent.

(a) The Remarketing Agent shall not be required to establish the Applicable Rate or calculate the Maximum Rate during the Current Special Rate Period.

(b) During the period from (and including) June 22, 2022 to (but excluding) the day that is seven days prior to the end of the Current Special Rate Period, Section 5 of this Agreement shall be amended by replacing the fee rate of 0.05% with a fee rate of 0.00%.

(c) During the period from (and including) June 22, 2022 to (but excluding) the day that is seven days prior to the end of the Current Special Rate Period, Section 8 of this Agreement shall not be applicable.

(d) Except to the extent provided in the Current Notice of Special Rate Period, Section 2(q) of this Agreement shall not be applicable during the Current Special Rate Period.

(e) Beneficial Owners and Holders shall not have the right to tender their VRDP Shares for Remarketing pursuant to an Optional Tender during the Current Special Rate Period.

(f) The provisions of the Related Documents relating to Mandatory Tender Events and related Mandatory Tenders shall be inapplicable during the Current Special Rate Period.

(g) Notwithstanding Section 2(m) of this Agreement, during the Current Special Rate Period, the Remarketing Agent shall not transfer or dispose of any VRDP Shares owned by the Remarketing Agent, except in accordance with Section 3.02 of Schedule III to the Fee Agreement, as if such Section 3.02 applied to the Remarketing Agent rather than the Liquidity Provider.

(h) Section 2(p) of this Agreement shall have no effect during the Current Special Rate Period.

(i) During the Current Special Rate Period, whenever the Fund intends or expects to include any net capital gains or ordinary income taxable for regular federal income tax purposes in any dividend on VRDP Shares, the Fund shall notify the Tender and Paying Agent of the amount to be so included (i) not later than 14 calendar days preceding the first SRP Calculation Date on which the SRP Applicable Rate for such dividend is to be established and (ii) for any successive SRP Calculation Date on which the SRP Applicable Rate for such dividend is to be established, not later than the close of business on the immediately preceding SRP Calculation Date. Whenever such advance notice is received from the Fund, the Tender and Paying Agent will notify each Holder and each Beneficial Owner or its Agent Member identified to the Tender and Paying Agent. Capitalized terms used but not defined in this Section 3(i) shall have the meanings given to such terms in the Current Notice of Special Rate Period.

(j) During the Current Special Rate Period, notwithstanding Section 6(b) or Section 9(b)(i), the Remarketing Agent may not have the right to resign or terminate to Remarketing Agreement as a result of the withdrawal of the VRDP Shares’ short-term preferred shares ratings by a Rating Agency, and there shall be no other consequences, penalties or notices thereof with respect to such withdrawal.

(k) During the Current Special Rate Period, the terms and provisions of the Current Notice of Special Rate Period shall be deemed a part of the Statement.

(l) In the event of any conflict between the terms of the Current Notice of Special Rate Period and the terms of the Remarketing Agreement (as amended by any amendments thereto) or the Related Documents (as amended by any amendments thereto), the terms of the Current Notice of Special Rate Period shall govern.

SECTION 2.03 Fees and Expenses.

The first sentence of Section 5 of the VRDP Shares Remarketing Agreement is hereby deleted in its entirety and replaced with the following:

Except as provided in the succeeding sentence, the Fund shall, except during the Current Special Rate Period, pay to the Remarketing Agent a monthly fee, payable in arrears in respect of a calendar month, for each VRDP Share Outstanding on the first calendar day of the immediately preceding calendar month, in an amount, equal to (a) the product of 0.05% of 101.85% of the Liquidation Preference for such VRDP Share and (ii) the actual number of days from and including such first calendar day of the immediately preceding calendar month to and including the last calendar day of such immediately preceding month, or if applicable, the date of any prior redemption of such VRDP Share (as the case may be) divided by (b) 365.

ARTICLE III.

MISCELLANEOUS

SECTION 3.01 Governing Law.

This Amendment shall be construed in accordance with and governed by the laws of the State of New York, without regard to conflict of laws principles that would require the application of the laws of another jurisdiction.

THE PARTIES HERETO HEREBY SUBMIT TO THE NON-EXCLUSIVE JURISDICTION OF THE FEDERAL AND NEW YORK STATE COURTS LOCATED IN THE CITY OF NEW YORK IN CONNECTION WITH ANY DISPUTE RELATED TO THIS AMENDMENT OR ANY MATTERS CONTEMPLATED HEREBY.

SECTION 3.02 Waiver of Jury Trial.

The Fund and the Remarketing Agent hereby waive trial by jury in any action, proceeding or counterclaim brought by either of the parties hereto against the other on any matters whatsoever arising out of or in any way connected with this Amendment.

SECTION 3.03 Successors and Assigns.

The rights and obligations of the Fund hereunder may not be assigned or delegated to any other person without the prior written consent of the Remarketing Agent and the Liquidity Provider. The rights and obligations of the Remarketing Agent hereunder may not be assigned or delegated to any other person without the prior written consent of the Fund and the Liquidity Provider. This Amendment shall inure to the benefit of and be binding upon the Fund and the Remarketing Agent and their respective permitted successors and assigns, and, subject to Section 24 of the VRDP Shares Remarketing Agreement, will not confer any benefit upon any other person, partnership, association or corporation other than persons, if any, controlling any Remarketing Agent within the meaning of Section 15 of the Securities Act, or Section 20 of the Exchange Act, or any Indemnified Person to the extent provided in Section 10 of the VRDP Shares Remarketing Agreement. As used in this Section 3.03, the terms “successors” and “assigns” shall not include any purchaser of VRDP Shares merely because of such purchase.

SECTION 3.04 Counterparts.

This Amendment may be signed in counterparts, each of which shall be an original, with the same effect as if the signatures thereto and hereto were upon the same instrument.

SECTION 3.05 Benefits.

Nothing herein, express or implied, shall give to any person, other than the Fund, the Remarketing Agent and their respective permitted successors and assigns, any benefit of any legal or equitable right, remedy or claim hereunder, provided, however, that the Liquidity Provider shall be an express third party beneficiary hereunder with respect to any notices required to be delivered to it hereunder and with respect to the representations, warranties and covenants of the Fund. Without limiting the generality of the foregoing, no Holder or Beneficial Owner (or their Agent Member) of VRDP Shares shall have or be deemed to have any right in respect of, or shall in any event be entitled to enforce or to seek recourse against any person in respect of, any provision of this Agreement, and any and all rights of holders of VRDP Shares or obligations of the Fund in respect thereof arise only under and as governed solely by the Articles of Incorporation, Articles Supplementary and by-laws as they are in effect from time to time.

SECTION 3.06. Consents.

The Remarketing Agent hereby consents to the he amendment to the VRDP Shares Fee Agreement, dated as of June 22, 2022, the amendment to the Tender and Paying Agent Agreement, dated as of June 22, 2022, and the Current Notice of Special Rate Period.

[Signature Page Follows]

IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be duly executed by their respective authorized officers as of the day and year first above written.

BlackRock MuniYield New York Quality Fund, Inc., as Issuer
By:	/s/ Jonathan Diorio
	Name: Jonathan Diorio
	Title: Vice President
TD Securities (USA), LLC, as Remarketing Agent

By:	/s/ Robert C. Franciscus
	Name: Robert C. Franciscus
	Title: Authorized Signature

[Signature Page – MYN Amendment to Remarketing Agreement]

EXHIBIT A