Last year, I owed $4000 tax to NY state and I paid it after filing 2020 tax return. Do I get credit or deduction for 2021 Federal or NY state tax?

[rjs]

On your New York state tax return you do not get any credit or deduction for tax paid to New York.

On your 2021 federal tax return you can include the tax that you paid to New York in 2021 in your itemized deduction for state and local income taxes. However, 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 addition, the deduction will not make any difference in your tax unless your total itemized deductions (after applying the $10,000/$5,000 cap) are more than your standard deduction.

[TomD8]

And you cannot deduct any interest or penalties that you might have been charged.  You can only deduct the actual taxes paid.

[Opus 17]

State income tax that you actually paid in 2021 is an itemized deduction on your federal tax return (if you itemize your deductions).  Taxes you actually paid include state withholding from your pay, plus any state tax payments.  Turbotax gets the withholding from your W-2 automatically.  To add the additional payment with your 2020 tax return, go to the Deductions page and look for "Estimates and other taxes paid."