PA and NJ have income tax reciprocity. So if you work in NJ, you would pay NJ income tax.
Living in PA, husband works in NJ (Or used to until O-Blame-O took over!!!!!), NJ income tax deducted from checks, we would file as a non-resident and all tax deducted is refunded. Reciprocal agreement is not mandatory by NJ employers, some won’t do it, too much paperwork for them I guess.
After getting the NJ tax refund, we then have to pay PA income tax, and a local township tax of 1% of earned income.
Also living in PA but working in NJ, PA taxes are supposed to be paid quarterly. We get forms/payment coupons to make payments towards our estimated taxes but we haven’t paid in advance yet, especially since husband has not had much work since O-Blame-O, hard to estimate the unknown. They usually have you estimate your taxes on the previous years income. We have paid a $60 penalty for not paying in advance.