Since you switched offices at the same time you switched your place of residence, you should file as a part year resident for New York and New Jersey. The income you earned in New York as a New York resident is New York sourced. The income you earned in New Jersey as a New Jersey resident is New Jersey sourced. Each return will reflect your income sourced in each state.
Furthermore, as a resident of New York, you did not earn income in New Jersey or pay New Jersey tax and vice versa. The credit of taxes paid to another state is when residents of one state are allowed a credit for paying taxes to another state. It prevents double-taxation on the same income. Your situation does not fit the criteria for this credit. Please remove any of these amounts from your return.
Your allocation on your part-year resident returns would be the amounts earned in each state during the time you were a resident. For additional information, please see How do I allocate (split) income for a part-year state return? and How do I file a part-year state resident return?
@nj30
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