You may have been able to claim a credit on your state resident return for the taxes you end up paying in PA.
Once you complete your PA return, you can always go back and amend your New Jersey return to claim a credit for the taxes paid in PA, if any.
It will not affect your federal or New York nonresident return so you would not need to amend those.
I have attached a link with instructions for amending your state returns.
Steps to amend a state return
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