When you have NY income reported on your W-2, the state requires that NY state wages in box 16 equal the amount in box 1 - even if you were a part year resident or nonresident for the year. You'll have to allocate your income properly within the New York state return section.
Since you have an assigned office within New York, you may be subject to the convenience of the employer rule - which means that any income that you earn for a New York based employer is considered New York source income and therefore taxable to New York. This is true even if you worked 100% remotely out of the state.
The same income would also be taxable in New Jersey, since you lived there. To avoid paying tax twice on the same income, you'd qualify for a credit on your New Jersey return for some of the tax paid on your New York return.
