NJ and PA are reciprocal states. You employer should not be withholding PA state tax. If they mistakenly withhold PA state tax, you have to file a PA non-resident return to get a refund. NJ will not give you a credit.
The reciprocal agreement between PA & NJ does not apply to city tax. You can claim a credit for any tax paid/withheld for a PA city (e.g. Philadelphia).
Reference: https://www.nj.gov/treasury/taxation/njit14.shtml#:~:text=NJ%20Taxation&text=If%20you%20are%20a%20Ne....
