New York requires employers to report total wages in W-2 Box 16. However if your employer said you made $9,000 in New York then you can allocate your wages in the New York section.
Your NY income may not match what your employer is reporting if you are allocating by days. That's fine. You can also allocate by percentage.
New Jersey residents are taxed on income earned anywhere so your will report all your income. You can claim a tax credit on the NJ return for the double-taxed $9,000 and tax paid to NY on that amount.
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