You report state income tax payments on your federal tax return for the year in which you pay the state tax, no matter what year the payments are for. You will not be able to deduct the full amount that you paid. For 2018 through 2025, the total deduction for state and local taxes is limited to a maximum of $10,000 per year ($5,000 if you are married filing separately). The maximum applies to the total of real estate tax, personal property tax, and either state and local income tax or state and local sales tax. In TurboTax enter the full amount that you paid. The limit will be applied on Schedule A.
Since state tax is an itemized deduction, it will not give you any benefit on your federal tax return unless your total itemized deductions are more than your standard deduction (after applying the $10,000/$5,000 limit to the state tax).
