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As rjs noted, it appears that you are a NJ resident and the period spent in PA was a temporary absence from your resident state for medical reasons. It also appears that you should have been filing in the past a NY non-resident return and a NJ resident return with a credit for taxes paid to NY.
Since PA and NJ have a reciprocal agreement, wages earned in PA by a NJ resident are not taxable by PA. If any PA income taxes were withheld, you would file a PA return requesting a full refund (easy to file a paper PA return). You would continue to file the NY non-resident and NJ resident returns.
https://www.state.nj.us/treasury/taxation/njit25.shtml
https://revenue-pa.custhelp.com/app/answers/detail/a_id/853/kw/nj%20reciprocity
As rjs noted, it appears that you are a NJ resident and the period spent in PA was a temporary absence from your resident state for medical reasons. It also appears that you should have been filing in the past a NY non-resident return and a NJ resident return with a credit for taxes paid to NY.
Since PA and NJ have a reciprocal agreement, wages earned in PA by a NJ resident are not taxable by PA. If any PA income taxes were withheld, you would file a PA return requesting a full refund (easy to file a paper PA return). You would continue to file the NY non-resident and NJ resident returns.
https://www.state.nj.us/treasury/taxation/njit25.shtml
https://revenue-pa.custhelp.com/app/answers/detail/a_id/853/kw/nj%20reciprocity
Based on the information you provided in the comments, you have to file a NY nonresident tax return as well as a NJ resident tax return, as re2boys said. The NY tax that was withheld will go towards the tax on your NY nonresident return. You will get a credit on your NJ return for part or all of the tax that you pay to NY. Prepare your NY nonresident return first, then your NJ resident return.
It looks like you do not have to file a PA tax return.
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