You can only claim a CREDIT in NY. If you claim the deduction instead, you will not get anything additional in NY. See this website: <a rel="nofollow" target="_blank" href="
https://www.tax.ny.gov/pit/credits/claim_of_right_credit.htm">https://www.tax.ny.gov/pit/credits/cla...>, and download this form <a rel="nofollow" target="_blank" href="
https://www.tax.ny.gov/pdf/current_forms/it/it257_fill_in.pdf">https://www.tax.ny.gov/pdf/current_fo... will probably want to calculate the form manually,because you will need to enter manually into TurboTax directly onto the electronic form (IT-257).
There is a section on the New York Return that discusses Other Deductions and Credits, where you can select Other Less Common Credits such as this one. After clicking start, and selecting No on the next screen (assuming your claim of right was not due to you defrauding the government or some other crime,) then you will click on the 5th box, Claim of Right Credit. This will allow you to input directly onto the form (manual calculations).
Of course, if you have the TurboTax program from the year in question, you can run a mock amended return to find out the amount of change between the different types of tax by reducing the amount of w-2 pay by the amount you had to repay. This will recalculate the NY tax, and the difference you will claim by filling out the correct information on the form. On this comment I cannot provide screenshots, but if you can't find the information I will be happy to post them.
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