If you physically work in NJ, then you would need to pay taxes in NJ. In this situation you will need to file both a NY Resident Return and a NJ Non resident return. You will report ALL of your income on both your NJ and NY returns. You will file your NY return first and then take a credit on your NJ return for taxes paid to NY.
You may or may not still end up owing money to your resident state depending on whether or not their tax rate is higher or lower than your nonresident state. If the non resident state had a higher tax rate than your resident state, your credit will be limited to the amount of tax you would have paid to your resident state. They will not give you a refund of the taxes you paid to the nonresident state.
Multiple States
If you are working in an office in NY for a company headquartered in NJ, then you would not need to pay taxes to NJ.
In this situation, you would remove the income from NJ and list it as $0 earned in NJ, you would then leave the taxes withheld as is and get a full refund of the taxes withheld for NJ that you did not need to pay. In this situation, you should update your withholdings with your employer. Having taxes withheld for the correct state helps to avoid underpayment penalties.
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