As I said above, you cannot legally claim the credit on your New Jersey tax return for the tax that you pay to New York. One of the requirements for the New Jersey credit is that "The income must have been properly taxed by the other jurisdiction." [NJ-1040 instructions, page 31, italics added] But New Jersey Division of Taxation Publication GIT-3W, page 5, says "another jurisdiction may properly tax a nonresident's income from: Services rendered within that jurisdiction." But your services are rendered in New Jersey, not in New York. Since the services are not rendered within New York, according to New Jersey tax law the income from those services is not "properly taxed" by New York, even though you pay New York tax on it. Therefore that income, the income you earn for working in New Jersey, cannot be used to calculate the credit for tax paid to New York.
Consult a local tax professional or a tax lawyer to see if there is any legal way to avoid paying tax to both states on the same income.
