NJ residents are not subject to PA income tax on their W-2 salaries or wages. The two states have tax reciprocity.
If PA taxes were mistakenly withheld from your pay, then in order to obtain a refund you must file a non-resident PA tax return on which you declare zero PA income, in order to obtain a refund. You cannot claim a credit on your NJ return for taxes incorrectly withheld for PA; you must claim a refund from PA.
Your income remains fully taxable by your home state of NJ.
File PA Form REV-419 with your PA employer to prevent PA withholding in future. Here's a link to that form:
https://www.pa.gov/content/dam/copapwp-pagov/en/revenue/documents/formsandpublications/formsforindiv...
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
