If you live in New Jersey, but you are employed in New York, you’ll file a New Jersey resident return, which taxes ALL your income. You’ll also have to file a nonresident return for New York, paying taxes on the income you earned in New York.
While it may seem like you are paying taxes on the same income twice, you’re given the ability to claim a credit for the taxes paid to New York.
New Jersey residents are allotted a tax credit for any income taxes paid to New York. This credit is deducted on the New Jersey schedule NJ-COJ.