I reside in NJ but have a part time job in NYC, I received two W2 forms from this employer, on both copies denotes different state wages and state income tax in boxes 16 and 17, my question is do I file both?

You must file state returns for both NJ and NY.

You report all income on both returns, but you pay taxes only on the NY-sourced income on the NY return.

On the NJ return, you pay taxes on all of your income, but you can claim a credit for the taxes paid to NY.

If this sounds too complicated, I recommend you get professional help.

I have experience filing both states, so if you want my professional help, email me at the email address in my profile.