Thanks for your concern.
Since you lived in both New Jersey and New York for part of the year, you would file a Part-Year Resident State Return to both states.
You will need to Allocate Your Income to report what was earned while a Resident in Each State.
You could end up owing one state, and getting a refund from the other, depending on which state you paid taxes to.
Since you already filed your Federal Return and New Jersey return, you can open TurboTax and review your NJ return to see if you need to Amend your State Return, based on the Allocation.
Click this link for more info on How to file a Part-Year Resident Return.
This link gives instructions on How to Amend a State Return.
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