Yes, if you only paid New Jersey tax on your income, the Total Payments under New Jersey Withholding would be the amount of tax credit for New York (they should be the same amount).
However, your 'New York Total' should be only the amount earned while you lived in New York. 'Portion taxed by New Jersey' would be the same amount (if you only paid tax to NJ on your income).
In the New York interview, TurboTax should display your Federal income and ask you to fill in the amount that belongs to New York.
If this is not evident from your W-2, you may need to do some calculation to determine the amount you earned while you lived in New York to enter here.
Click this link for more info on Allocating Income as a Part-Year Resident.
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