Company: MYI
Filing Date: 2025-02-28
Form Type: N-23C-2
Source: 0001193125-25-042184
Chunk: 1

Company: BLACKROCK MUNIYIELD QUALITY FUND III, INC.
Filing Date: 2025-02-28
Form: N-23C-2
Chunk 1
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 of shares and the basis upon which the securities to be redeemed are to be 
 selected:                                                                                                 |

The Fund may redeem up to 67% (2,387 shares) of its currently outstanding Series
W-7 VRDP Shares. Such redemptions(s) will be made on a pro rata basis among the Holders of the Series W-7 VRDP Shares. Holders of the Series W-7 VRDP Shares will receive the liquidation preference of $100,000 per share, together with accumulated and unpaid dividends through the date of redemption. All of the Series
W-7 VRDP Shares are held in book-entry form through the Depository Trust Company (“DTC”), and such shares being redeemed will be redeemed in accordance with the procedures of DTC. Payment by the Fund
of the Redemption Price (as defined in the Articles) will be made to The Bank of New York Mellon, as tender and paying agent for the Series W-7 VRDP Shares.

Pursuant to the requirement of Rule 23c-2 of the Investment Company Act of 1940, the BlackRock MuniYield Quality Fund
III, Inc. has duly caused this Notification of Redemption of Securities to be signed on its behalf by the undersigned, thereunto duly authorized, in the City of New York, and the State of New York, on the 28 day of February, 2025.

| BLACKROCK MUNIYIELD QUALITY FUND III, INC. |     |                     |     |                 |
| By:                                        |     | /s/ Jonathan Diorio |     |                 |
|                                            |     | Name:               |     | Jonathan Diorio |
|                                            |     | Title:              |     | Vice President  |

[Signature Page – MYI 23c-2 Notice]