Are you sending a copy of your New York return to New Jersey? NJ will not accept the credit for taxes paid to another state without a copy of the other state’s return.
We’d have to know what the letter says, but it sounds like NJ denied your credit (set it to $0) because they do not have a copy of the New York return. NJ will restore the credit if you send a copy of the NY return. That is usually mentioned in the letter.
TurboTax will send the NY return electronically if you e-file your NJ return. Sometimes NY gets lost.
The other problem may be that you are claiming your entire NY withholding (W-2 Box 17) as tax paid. You can only claim your NY tax liability in the other state tax credit (withholding minus refund).
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