when will my state income tax be paid from my checking account

If you want to check the debit date you specified, look on the filing instructions for your return.  It will tell you the debit date the IRS or State will deduct the payment.  If you did not print them out you can view them using the following steps: 

 
TurboTax Online 

1. In TurboTax Online, sign into your account.
2. You should be on your Tax Home page.
3. Scroll down to Your tax returns & documents.
4. Select 2024, and then select Add a State (you're not actually adding a state, this just gets you into the right menu).
5. Once you're in your return, you can navigate around as usual.
6. Click Tax Tools (in the black bar on the left of your screen) and then click select Print Center.
7. Click Print, save or preview this year's return

TurboTax CD/Download 

1. Go into Forms Mode by clicking on the Forms icon in the top right of the blue bar.  
2. In the Forms in My Return list on the left, click Filing Inst.  [It's usually toward the bottom of the list.]  The form will appear on the right side of the screen.
3. You can view the form on the screen or you can print a copy by clicking the Print box at the bottom of the screen.
4. To return to the interview, click on the Step-By-Step icon in the top right of the blue bar.

This did not tell me when to expect the debit to my account, I ended up calling TuboTax and they advised I would just need to wait to see.  They KY state site wouldn't let me create an account for some reason, but after a couple weeks my account was debited.