I paid 2023 property tax in January 2024 after receiving the tax bill. Does this payment go on 2023 filling or on the 2024 filling?

Property tax goes on your tax return for the year that you paid the tax. The property tax that you paid in 2024 goes on your 2024 tax return, no matter what year the tax was for.

Property tax is an itemized deduction. It will not affect your tax if you are not itemizing deductions. You can enter the property tax, and any other itemized deductions that you might have, and let TurboTax figure out whether your total itemized deductions are more than your standard deduction.

Even if you do not itemize deductions on your federal tax return, the property tax might make a difference in your state tax return in some states.