You will file a NJ return with $0 income for the period you had NJ taxes withheld. NJ and PA are reciprocal states, so you only pay tax in PA, not NJ. But since they mistakenly withheld the NJ tax, you have to file a $0 return to get the taxes returned to you. Fortunately your employer has corrected this so that going forward you will only have to file in PA.
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