Since all your income was earned in New York, prepare your Part-Year New Jersey return first.
If New Jersey wants to tax part of your NY income (based on residency), then in the New York return, when asked about 'credit for taxes paid to another state' enter the amount that New Jersey wants to tax you and indicate New Jersey.
Click this link for more info on How to file a Part-Year Resident Return.
[Edited 03/18/2020 | 3:33 PM]
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