You need to put it in as a state extension payment for your 2020 state taxes...that's the only way the state forms will know to give you credit for having made that payment.

When you put in the state extension payment  (on the  Federal Deductions&Credits page ), you will also put in the correct January 2021 payment date.   That 2021 date lets the Federal software automatically know to not use that payment as a federal 2020 deduction.    AND, if you use TTX next year and transfer in the final 2020 datafile you are creating, then that 2021 state extension payment should automatically show up in the 2021state payment deductions....though you will need to confirm it's there, in case there is a software "fumble" that misses it.

Thank you for the reply!

Is there any workaround to report this deduction this year to lower my fed taxes?

It's theoretically a payment I made in regards of my 2020 income after all. 

Nope...if the payment was made in 2021, even if FOR 2020 state taxes, it isn't a Federal income deduction for 2020 taxes....it's only used for 2021.     When I make such State payments, I usually make them in December, for that reason, and to keep things clearly and cleanly assigned to the year I'm working on.

Good advice... Thank you! Appreciate the time you took to help me