It depends on whether you still worked in New York after you moved to New Jersey.
If you moved to New Jersey and got a job in NJ, then you have no double taxed income. All your New York income goes on the NY part-year return and all your New Jersey income goes on your part-year NJ return.
If you moved to New Jersey and continued to work in New York (either physically or in some cases, remotely), then your double taxed income will be the amount of NY income you earned while living in NJ.
Use income and tax from your NY tax return to calculate the credit for New York tax on your New Jersey tax return.
Find the percentage of NY income earned in NJ and multiply that percentage by the total tax on your NY tax return. For example, if you earned 50% of your NY income while living in NJ, then you can claim a credit for up to 50% of NY tax.
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