I am an independent contractor and I am being paid by my contracting company on a 1099-NEC. If I make estimated quarterly payments when I file my taxes (usually April 15) How will the tax software know I paid those quarterly taxes already?
it won't know since Turbotax and virtually all other tax apps don't assume the payments are made. you'll have to enter them on the tax payments worksheet. in step-by-step mode Turbotax should ask you if you made these payments. then it will take you through entering each payment amount and the date. if you pay state estimates you also have to enter those.
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.
OR
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.