It depends. You are not taxed in NYC unless you are a resident of NYC, and you are not taxed in Yonkers if you did not live or work in Yonkers. If that situation applies to you, then you want the "incorrect" W-2 that shows the NYC or Yonkers' withholdings. Please click on this website for more information: New York City, Yonkers and MCTMT - Department of Taxation and ...
In TurboTax, you will enter your W-2 as it appears, with a box 20 entry of either NYC if your W-2 says New York City (or any of the 5 boroughs) or Yonkers if it says Yonkers. When you prepare the New York resident return (for New York State), NYC resident and Yonkers resident or nonresident wage tax is reconciled as part of the state return. Therefore, if you were not an NYC resident, and did not either live or work in Yonkers, any taxes withheld to either of these municipalities will be included as part of your NYS refund (your refund will be increased by the mistaken city withholdings).
It is good that you have corrected this going forward with your employer, as you do not want these taxes withheld if you do not have to pay them. However, if you did pay in on them last year, you want that included on the return so that the amount you paid is fully refunded.
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