Federal taxes owed and paid for a prior tax year are not entered on federal tax return.
State taxes owed and paid are entered on Schedule A as an itemized deduction for the tax year paid. So if you paid additional state taxes for the 2022 state tax return in 2023, you will need to amend the 2023 return to add the payment on the 2023 Schedule A.
See this TurboTax support FAQ for amending a prior year tax return - https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-return/amend-change-correct-return-a...
