You will need to file a non-resident tax return for New York State, that will include New York City, to get a refund of the taxes paid to them. If you don't have any state or local taxes withheld for New York listed on your corrected W-2 form, you should enter them in box 17 and 19 on your W-2 form entry. Also, enter the State abbreviation in box 15 and "NYC" in box 20. Even though that won't agree with what is on your W-2 form, the state will have a record of the taxes paid in so your return will line up with what they show for you.
New York will show all of your income as taxable, but you will be asked to enter the income earned in and out of New York, and your tax will be adjusted based on the percentage of income earned in New York. So, you won't have any tax in New York and New York City, so all of your tax paid in should be refunded.
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