The fourth quarter estimated payment for tax year 2021 is due Jan 15, 2022. Whether you paid it 12-1-21 or 1-15-22, it's still for tax year 2021.
In TurboTax (TT), you use the actual date paid, in your case 1-15-22. Note that in the TT menu, you are entering 2021 tax year payments.
