The $6,589 probably should go in the second box on the Medical Expenses screen in the New Jersey interview. That's the box that says "New Jersey medical insurance premiums included in your New Jersey wages but not in your federal wages on your W-2, and not deducted on Federal Schedule A." That is normally the case in New Jersey. Medical insurance premiums are pretax for federal but after tax for the state, so they can be added to the medical expense deduction on the New Jersey tax return.

If your NJ wages in box 16 of your W-2 are exactly $6,589 more than the federal wages in box 1, then the difference is surely due to the medical insurance premiums and you can enter the amount of the premiums in that second box on the TurboTax screen. If the difference between box 1 and box 16 is not exactly equal to the medical insurance premiums, ask your employer if the premiums were included in box 16 but not in box 1. If so, you can enter them in the second box on the TurboTax screen.