I'm not 100% clear about your facts. I think you are saying you got a NY refund and had to pay NJ. The principle is that if you itemized in 2017 you would have had to include any NY and NJ income tax payments made during 2017 on your Schedule A. Getting a state or local refund means you effectively subtracted too much state and local tax from your 2017 income. The tax code adjusts for this by adding the over-itemization amount back into 2018 income. (There is a special case if removing the refund from 2017 would have made the standard deduction larger.) Bottom line, I would add the amounts on any forms 1099-G you received for what to enter on Schedule 1, line 10.
