I'm a graduate student who goes to school in Pennsylvania. Do I need to file state taxes for Pennsylvania?

[collabean]

I receive a stipend from my university which is my form of income. I have had income taxes deducted from my paychecks to PhilaNR and GradPhi. My permanent residence is in New Jersey. Last year I didn't file taxes for PA as my NJ tax return took into account the taxes I paid from my W2 (note my W2 for 2021 only paid income tax PhilaNR). This year after entering my W2 it says I owe taxes to NJ. Do I need to file a PA tax return for my NJ return to recognize the income tax I've paid already?

[MonikaK1]

Under the terms of a reciprocity agreement between New Jersey and Pennsylvania, compensation paid to Pennsylvania residents employed in New Jersey is not subject to New Jersey Income Tax under the terms of the Reciprocal Personal Income Tax Agreement between the states. Similarly, New Jersey residents are not subject to Pennsylvania income tax either. Compensation means salaries, wages, tips, fees, commissions, bonuses, and other payments received for services rendered as an employee.

If you are a New Jersey resident and your employer withheld Pennsylvania income tax from wages, you must file a Pennsylvania return to get a refund. To stop the withholding of Pennsylvania income tax, complete Form REV-419EX, Employee’s Nonwithholding Application Certificate, and give it to your employer. 

Please see this New Jersey webpage for more information.

See also this TurboTax article and this one on multiple-state situations.

[Hal_Al]

Q. Do I need to file state taxes for Pennsylvania?

A. No, because of the reciprocity agreement and the fact that no PA state tax was withheld (so, you don't need to file for a refund of PA state tax).

The reciprocity agreement does not apply to city tax.  So, your employer was correct to withhold city tax.