Assuming you are speaking about entering an estimated tax payment in TurboTax in the "Deductions and Credits" section. There is no option to say the tax payment is applied to tax year 2023 in the 2022 tax return. The date entered is the date paid which could be January 2023. However, when you enter an estimated payment in the "Estimates and Other Taxes Paid" topic it will reduce your 2022 tax.
Once you enter a payment it reduces the 2022 tax bill no matter what date you enter as the date paid. So the date entered doesn't matter on your tax return for the tax due but the date(s) entered could affect an underpayment penalty if there is one calculated on your return.
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