You seem to have two different questions here. As far as a tax credit or deduction is concerned, you don't get any more credit for making estimated Federal tax payments than what you would for having Federal Tax withheld from your paycheck. It is a "credit" towards your tax obligation. State estimated payments can count as a deduction on your Federal Return, if you itemize your tax deductions, and to the extent that those deductions do not exceed the SALT limit of $10,000 in a year. (For the state return, the effect is the same as the Federal estimated payments).
As far as tracking them is concerned, TurboTax can't track them, because TurboTax cannot verify that they are actually paid. TurboTax can set up the payments to be deducted electronically, and TurboTax can carry the information forward to next year, but you will need to keep track of the estimates that are actually paid. A worksheet can print out to help you to do so.
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Well you get a Deduction for them in the sense that they are deducted from your tax due like withholding from W2 or 1099R. You have to manually enter them.
You can type estimates paid in the search box at the top of your return and click Find and it will give you a link to Jump To it.
To enter Federal or State Estimated Taxes Paid, including a state estimated payment made in January for the prior year, go to
Federal on left or at top. Personal (Home & Business)
Deductions and Credits at top
Then scroll way down to Estimates and Other Taxes Paid
Estimated Taxes - click the start button
For 2020 Federal Estimated payments should be on 1040 line 26.
You enter state estimated payments under the federal side (because they can be a federal itemized Deduction). THEN after you finish filling out the estimates under Federal you need to click on the State Tab at the top and start the state return over for it to update.