1) PA and NJ have a reciprocal tax agreement, whereby PA residents working in NJ are only taxed by their PA home state. (and the reverse applies for NJ resident working in PA). SO if no NJ wages are being reported on the state line of your W-2 forms (boxes 15,16,17), then no NJ non-resident tax return is required. IF NJ withholding was accidentally done, then you would have to file NJ-NonResident, but report it as zero wages, to get all of the NJ withholding refunded.
2) Certainly, it is possible to owe PA most any amount, if PA taxes were not withheld at a high enough level. With part time jobs, perhaps no PA taxes were withheld..or a lower rate than usual since the employer cannot know you were working multiple jobs. OR....some employer properly didn't withhold NJ, but wasn't setup to withhold PA taxes either.... OR...if the NJ job accidentally did withhold NJ taxes....then you owe PA taxes on all that income because PA expects you to get that improper NJ withholding refunded to you, since it shouldn't have been withheld for NJ in the first place.
IF NJ withholding was done for one or both those NJ jobs, you need to get it stopped in the future.....Get the form NJ-165 filed with that employer...and some employers can also withhold PA taxes too:
Employee’s Certificate of Nonresidence In New Jersey, Form NJ-165 (state.nj.us)
____________*Answers are correct to the best of my knowledge when posted, but should not be considered to be legal or official tax advice.*
