How do I enter payments with state extensions?

Where are you entering it?   To enter the amount you paid with an extension (including state extension)  go to

Federal Taxes (or Personal for desktop H&B version)

Deductions and Credits

Then scroll way down to Estimates and Other Taxes Paid

Other Income Taxes - Click the Start or Update button

Next page second section Payments with Extension

Either Visit All or Click Start or Update by the extension you paid

Pay attention to which year you are entering for a State Extension payment.  A prior year state extension payment is also deductible on the federal return so be sure to enter it here.

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.

Since you've made multiple state extension payments, you will need to enter the total amount of state extension payments you've made. The program will enter this total on your federal return but you will need to go to each state return and enter the extension payment in the state interview for it to be accurately reported on yout state return.

For Online versions:

Although tedious and buried in TurboTax online, you can enter in payments made with extensions for multiple states.  You have to go into the interview for each state and get to the section regarding filing an extension.  Once there, you will need to say you are going to file an extension and then it will eventually trigger a screen asking for the payment amount you will make with the extension.  Once the amount is entered it will populate on the corresponding form and you should see the TurboTax refund meter adjust accordingly.

To enter, change or delete a payment made with an extension request (Federal, State, Local) -

Click on Federal Taxes (Personal using Home and Business)
Click on Deductions and Credits
Click on I'll choose what I work on (if shown)
Scroll down to Estimates and Other Taxes Paid
On Income Taxes Paid, click on the start or update button

On the next screen select the type of extension payment made and click on the start or update button

Or enter federal extension payment in the Search box located in the upper right of the program screen. Click on Jump to federal extension payment

@adammacks 

When you enter the total amount of the extension payments in the federal return it asks what state it was for. In the drop-down list select "Multiple States," at the very bottom of the list. The payment amount will not flow to the state return.

You didn't say whether you are filing New York as a resident or a nonresident. You also didn't say whether you made estimated tax payments to New York. I suspect you did, because that makes it more difficult, but not impossible, to enter the payment with an extension.

On a New York resident return, Form IT-201, the total of estimated tax payments and the payment with an extension goes on line 75. On a New York nonresident return, Form IT-203, the total of estimated tax payments and the payment with an extension goes on line 65.

Go to forms mode and open Form IT-201 or IT-203, whichever one you are filing. In either case, resident or nonresident, if you did not make estimated tax payments the line for the payments will be blank. Just click on the appropriate line and type the amount of the extension payment. Do not double click, QuickZoom to another form, or go to another form in any other way. You can just enter the amount directly on IT-201 line 75 or IT-203 line 65.

If you did make estimated tax payments, the total of the estimated tax payments will be on the appropriate line and you cannot change it directly. Open Form IT-370, which is the extension form. Check the box at the top that says "Check this box to freeze the amounts flowing to this form." You can now change the amounts in the IT-370 Smart Worksheet. On line 1 of the worksheet enter the amount that you paid with the New York extension. If there are any amounts on lines 2 through 5 change them to zero. On line 7 enter zero. Line 8 should now be the amount that you paid with the extension (the same amount that you entered on line 1) and that amount will be added to the total payments on IT-201 line 75 or IT-203 line 65.