With regard to crediting the payment to your 2023 state tax, see the reply from DoninGA above.
However, if you are itemizing deductions on your federal tax return, you have to include the state tax payment in your itemized deduction for state and local taxes in the year that the payment was actually made. So you could end up with a payment of 2023 state tax that is deductible on your 2024 federal tax return, not on your 2023 federal tax return.
