The UI and family leave taxes should be based on the state where you worked, not where you lived. Did you work part of the year in NY and part of the year in NJ? If so, you have to pay the taxes for both states.
But if you worked in the same company location all year, you should only pay the UI and FLI taxes for the state that you worked in, even though you lived in two different states. If your employer incorrectly withheld UI and FLI taxes for a state that you did not work in at all, you should ask the employer to give you a refund of the incorrectly withheld taxes, and give you a corrected W-2.
