If your job was in New York, you file as a part-year resident of New York, but pay NY state taxes on the entire amount of your 2019 income. While you were living in NY, the income was taxable in NY as both "NY resident and NY source". While you were living in NJ, the income was taxable in NY as "NY source".
For NJ, you file a part-year resident return, but pay NJ taxes only the income earned while you lived in NJ. You will get a credit on your NJ return for the portion of your income taxed by both NY and NJ, i.e., earned while you lived in NJ. That way, you don't pay state tax twice on the same dollar of income.
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