UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

SCHEDULE 14A INFORMATION

Proxy Statement Pursuant to Section 14(a) of the

Securities Exchange Act of 1934

Filed by the Registrant  ☒

Filed by a Party other than the Registrant  ☐

Check the appropriate box:
☐    Preliminary Proxy Statement	☐    Confidential, for Use of the Commission Only (as permitted by Rule 14a-6(e)(2))
☐    Definitive Proxy Statement
☒    Definitive Additional Materials
☐    Soliciting Material Pursuant to § 240.14a-12

BLACKROCK MUNIHOLDINGS NEW YORK QUALITY FUND, INC.

(Name of Registrant as Specified In Its Charter)

(Name of Person(s) Filing Proxy Statement, if Other than the Registrant)

Payment of Filing Fee (Check the appropriate box):

☒ No fee required.

☐ Fee paid previously with preliminary materials.

☐ Fee computed on table in exhibit required by Item 25(b) per Exchange Act Rules 14a-6(i)(1) and 0-11.

Your Vote Matters BlackRock Municipal Closed-End Funds Vote now to reduce costs for your Fund and to stop receiving solicitation notices Why am I receiving this letter? You are a shareholder of one or more of the following funds and entitled to vote at the upcoming special shareholder meeting on October 15, 2025: BlackRock New York Municipal Income Trust (BNY) BlackRock MuniHoldings New York Quality Fund, Inc. (MHN) BlackRock MuniYield New York Quality Fund, Inc. (MYN) What am I voting on? Shareholders are being asked to approve combining the funds to realize potential benefits for you as a shareholder, including: Lower expenses, ranking in the 1st quartile among peers Enhanced trading on exchange Implementation of a discount management program How do the Boards recommend that I vote? The Board of each Fund unanimously recommends that you vote “FOR” each applicable Proposal. If you have any questions on how to vote or about the proposals to be voted on, please contact Georgeson LLC at 1-888-686-6228. The proxy materials previously sent to you contain important information; please read them carefully. Copies of the Proxy Statement are available for free on the Securities and Exchange Commission’s website at www.sec.gov or by visiting WWW.PROXY-DIRECT.COM/BLK-34670 or by calling Georgeson LLC, the Funds’ proxy solicitor, toll free at 1-888-686-6228. Voting is simple Vote online By scanning the QR code or using the website provided on the enclosed proxy card or voting instruction form Vote by phone By calling the toll-free number on the enclosed proxy card or voting instruction form or downloading the ProxyVote app Vote by mail By completing and returning the enclosed proxy card or voting instruction form in the pre-paid envelope provided