You will file a Part-Year New York and Part-Year New Jersey (which is really a NJ Resident return showing income for the part of the year that you lived there). Since you worked in New York, you will report the January to August 2021 income and then the September to end of year income as nonresident NY state source income. On your NJ return, you will report the September to December income, and claim a credit for taxes paid to another state based on the taxes you paid on that specific income.
NOTE: You will want to complete the New York tax return first.
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