ALL your income is subject to NY tax, no matter where you earned it, because you are a NY resident. You get a credit on your NY resident tax return for part or all of the tax that you pay to NJ. (It's called the "resident credit" and it's on Form IT-201 line 41.) You might still owe some tax to NY because NY tax rates are higher than NJ.
New York and New Jersey do not have a reciprocal agreement. That's why you have to file tax returns in both states.
