As @DanielV01 mentioned, New Jersey and Pennsylvania have a reciprocal agreement, so no PA income tax should have been withheld on your W-2, regardless of your New York situation.
If PA tax was withheld in error, you will have to file a non-resident PA income tax return (PA-40) to get a full refund of your withholding. To do this,
- Go to the screen Compensation Summary and click Edit,
- On Verify Income, check Entire amount of this income is not taxable in PA.
This will create a non-resident PA tax return with $0 wages.
Mail your PA return to Harrisburg along with your W-2 and a copy of your New Jersey return, showing all the income was properly reported to PA. You can e-file, but if so, you may receive a letter from PA asking why your reported $0.
Here are PA’s instructions:
If you are a resident of a reciprocal agreement state working or performing services in Pennsylvania and your employer withheld Pennsylvania income tax, you may request a refund of the Pennsylvania tax. You report zero taxable compensation on Line 1a and the Pennsylvania tax withheld on Line 13. Submit federal Form W–2 or a photocopy and a copy of the resident income tax return that you filed/will file with your resident state. Also, submit a statement explaining that you are a resident of a reciprocal agreement state.
Also complete REV-419, Employee’s Nonwithholding Application Certificate, and send it to your employer to discontinue PA withholding.
Prior years. Do not file any prior year PA forms. A NJ resident working in NY does not have any PA income and should not file a PA return.
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