Since PA  and NJ have a COMPACT stating "I won't tax yours and you won't tax mine," no employer should report both states nor withhold both states. If they do, they should hire a payroll service. 

Most of mine are NJ residents working in PA. No wages are taxable to PA, so enter PA wages and tax, file PA non resident and get all back. I always attach an Additional Info statement stating the obvious; employer messed up.

For NJ, then, file NJ resident. NJ wages line will count both PA and NJ wages from W2, so you need to check box on wage schedule to remove PA wages from being counted. Keep clicking magnifying glass on NJ wages line to get to schedule.

PA wages are rarely the same as NJ wages, unless there are zero deferrals or pre tax payments.

PA taxes all compensation, including pre tax medical, 401k and 403b deferrals. NJ taxes 403b deferrals AND pre tax medical, but does not tax 401k deferrals.