You didn't say why you are working remotely. It makes a big difference, because New York has a "convenience of the employer rule," but New Jersey does not agree with New York's rule. That creates a conflict that could be a big problem for you.
You also didn't say where you live. All of your income is always subject to tax by the state that you live in, no matter where the income is from. I assume that you live in New Jersey. If that's not correct, it could change the answer, so let us know what state you live in.
The usual rule in most states, including New Jersey, is that income is sourced from the state where you do the work. So if you work in New Jersey, the income you earn is from a New Jersey source, and is therefore taxable by New Jersey. It doesn't matter where the employer's office is located. You are doing the work in New Jersey. Since you also live in New Jersey, the income is only subject to New Jersey tax, and not to New York tax.
But New York does not follow that rule. According to New York tax law, the source of the income paid by a New York employer depends on why you are working in another state. If your employer wants you to work in New Jersey for business reasons, then you are working in New Jersey for the "convenience of the employer." In that case, the usual rule applies. You are employed in New Jersey and your income is from a New Jersey source. You would pay New Jersey tax on the income, and not New York tax. The business reasons could be because your employer wants to have a representative in New Jersey, perhaps to work with New Jersey customers, or to oversee some operations of the employer in New Jersey, or because the employer does not provide office space for you in New York and requires you to work at home.
If you are working in New Jersey for the convenience of the employer, you would pay only New Jersey tax. So you should have New Jersey tax withheld from your pay, and not New York tax.
On the other hand, if you are working remotely because that is your own preference, then it's for your own convenience, not the employer's convenience. In that case, since you are telecommuting to a New York office, New York considers the income to be from a New York source, the same as if you actually worked in the New York office. That makes the income subject to New York tax. But New Jersey does not agree with that. New Jersey considers it New Jersey source income, because you are doing the work in New Jersey. So New York says the income is from New York, and New Jersey says the income is from New Jersey.
If you actually worked in New York, New Jersey would recognize the income as New York income. You would pay New York tax on the income, and you would get a credit on your New Jersey income tax return for the tax that you pay to New York. The net result would essentially be that you would pay little or no New Jersey tax. But New Jersey only allows the credit for tax that you pay to New York on income that is "properly taxed" by New York. Since New Jersey considers the income to be from a New Jersey source, they do not consider it "properly taxed" by New York. Therefore they will not allow the credit on your New Jersey tax return. You would be filing your New York tax return as a nonresident, and the New York nonresident tax return does not have a credit for tax paid to another state.
So if you are telecommuting from New Jersey to New York for your own convenience, in order to satisfy the tax laws in both states you would have to pay tax to both New York and New Jersey on the same income. You would not get credit on either state's tax return for the tax paid to the other state.
Your employer, being a New York employer, has to follow New York law. The fact that they are withholding New York tax indicates that they are treating your income as New York income, even though you are working in New Jersey. Your W-2 will show New York income, so the state will see it that way.
There is no easy, legal answer to this situation. If you are telecommuting from New Jersey to New York for your own convenience, I suggest that you consult a local tax professional for advice on how to handle it.
