I work full time in NYC and I live in NJ. What did I put down for any federal deduction attributable to the period of your New York state nonresidency? Do I put zero OR the state taxes I paid in NY?
Since you worked the full-year in New York as a nonresident, you should enter the full amount of the deduction shown on the screen.
This screen can be a bit complex, but ultimately, it is questioning the amount of your deduction that was paid with the income you earned in New York. If you paid those state taxes with the money you earned in New York, then it should be entered into the New York Source Portion column.
If, on the other hand, you worked in NY from January - June, and those taxes were paid from July - December, you would enter 0. If you paid some of the deduction while working in New York, and some of it while not working in New York, then you would have to allocate it accordingly.
However, since you stated you worked full time in NYC, I am assuming you worked there throughout the year. Therefore, it should be the full amount.