You will not need to change anything when you enter the Forms 1099-NEC in the federal return.
When you fill out the My Info section, at the beginning, from the left menu bar, it will ask if you lived in any other states. If you answer Yes, it will generate questions when you are ready to enter your state Part Year returns for New York and New Jersey. They will each have a section where they will show your federal income by different types and ask which portion should be allotted to this state, so you are not double taxed for the same income.
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