If you made a payment when you filed the extension, just make sure TurboTax ultimately gives you credit for the payment.   It may populate the payment automatically for you.  If it doesn't, you can enter it (or check on it) as below:

Under the Federal Taxes tab (or Personal tab in Home and Business)
Click sub tab "Deductions & Credits."
"I'll choose what I work on."
Your 2018 Deductions and Credits summary page.
Scroll down to topic "Estimates and Other Taxes Paid."
Find subtopic ESTIMATES, and click START or Update.
The next screen is titled "Estimates and Other Income Taxes." Scroll down to "Payments with Extension."
Either click "Visit All", or choose the type of extension payment and click START (or Update).

Once you have entered (or confirmed if pre populated) the extension payment, then before filing verify that you are getting credit for it.  Look at Line 70 of your Sch 1 and verify that the Federal figure is correct.  A state extension payment is entered in the same navigation steps as above.  

To get the amount paid on a state extension to show up on the state return……
When you are done updating your federal return, you need to transfer the new federal information by going back through the state tab and the state return. Nothing will change until you transfer the fed info to the state again. If applicable, verify that it appears on the state return.

 Review the NY return ... what is on line 75 of the IT-201 ?  

You can peek at only the form 1040 & state summary page  by going here:

Click on Tax Tools >>>Tools >>>Click on View Tax Summary >>>Click on Preview my 1040

To view the entire return using the online editions before you file, you will need to pay for your online account.

To pay the TurboTax online account fees by credit card, without completing the 2017 return at this time, click on Tools … Then click on Print Center.  Then click on Print, save or preview this year's return.  On the next page, to pay by credit card, click Continue.  On the next screen it will ask if you want Audit Defense, if you do not want this option just click on the Continue button.  The next screen will ask for all your credit card information so you can pay for the account.

Another thought for state extensions.  Be sure to pick the right YEAR since you can also enter prior year state extension payments to be deductible on the federal return.