You'd file a return in both states: a New Jersey resident return and a New York nonresident return.
New York collects taxes on income you earned while working there. And while New Jersey requires that you report all of your income, including what you earned in New York, they'll give you a credit for your New York taxes so you don't get double-taxed.
Just make sure you prepare your New York nonresident return first, so we can apply the correct tax credit once you get to your New Jersey return.
