Taxes on paycheck

If you live and work in NJ, then you are subject to paying state income tax in New Jersey---not in PA.   

Thank you for answering, It looks like the company has messed up my paycheck, they took taxes from both states. ☹️ I will have to get this fixed.

It may depend on more details, such as the meaning of "agency I work for". 

See: https://ttlc.intuit.com/community/state-taxes/discussion/live-in-tx-work-remote-for-company-in-pa-do-i-pay-pa-state-tax/00/3240304

the agency is a temp agency that is located in PA, the actual company that I work for is located in New Jersey.

@loloj5050 --

Submit PA Form REV-419 to your employer to prevent withholding of PA income tax from your pay.  Here's a link to that form:

https://www.pa.gov/content/dam/copapwp-pagov/en/revenue/documents/formsandpublications/formsforindividuals/pit/documents/rev-419.pdf

"The agency is a temp agency that is located in PA, the actual company that I work for is located in New Jersey."

I agree with the others, they should not be withholding PA tax.   Don't be surprised if they can't or won't correct it, for what's already been done.  You may have to file a PA non resident return to get a refund.