It depends. Both NY and NJ are allowed to tax the income you earned inside of NY. NY will tax you as a nonresident, and NJ as a resident. However, NJ will provide a credit for the taxes that you pay to NY on this income. Because of this, you should prepare the NY return first, to assist in calculating this credit.
The NJ return does have a couple of key entries. If your NY W2 also had NJ in a box 15 on the form, with an amount in box 16, then, on the NJ return, you would get a screen asking you if all of the income were taxable to NJ. You would say no, and then mark the NY line as not taxable in NJ (so the system does not double-up the income). However, if your NY return does not have NJ in any box 15, then this screen will not appear. However, you will still get a question about double-taxed income. This is the NY income listed in box 16 on that form. That income is still being taxed in both states: NY and NJ. You will need to enter the amount so that TurboTax calculates the correct credit on the return.
Here is an FAQ on how to prepare a nonresident return: https://ttlc.intuit.com/replies/3302052
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