Can I report an excess Roth IRA contribution made in July 2020 for the 2019 tax year on my 2020 tax return? Or do I need to file an amended 2019 return?

Yes, you may report this in your 2020 return. To report, you will need to create a substitute 1099-R.

1. Open your return. 
2.  Inside TurboTax, search for 1099-R and select the Jump to link in the search results.
3. Answer Yes on the first screen
4. next screen choose I will choose to enter my form.
5. Next screen asks how you will like to enter this, indicate you will type it in yourself.
6. Next screen say its for you. Next screen indicate it's from a Financial institution>continue
7. Next is where you enter information. 
8. in order to create a substitute 1099-R, you will need to obtain and name, address, and payer TIN. Make sure you check the IRA/SIMPLE/SEP box. 
9. Next you will report the total amount of the distribution in Box 1 and the taxable interest earnings in Box 2A.
10. In Box 2 you will enter codes P and then in the second box below the first one, you will enter a J.
11. After entering, there will be a question asked what year on form 1099-R.  you will say 2021.
12. The next screen is where you will check that you are creating a substitute 1099-R
13. You will navigate and answer questions in the next few screens but you eventually come to a Substitute 1099-R agreement>continue\
14. Follow the directions given in the screens that follow to finish out this section.

[Edited 02-25-2021|12:11 PM PST]

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@aksnorth wrote:
Note, the full amount of the excess contribution, plus earnings, will be withdrawn before April 15, 2021 to avoid the 6% penalty.  I assume all earnings should be reported on the 2020 return, is this correct?

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No.    A contribution *for* 2019 had to be returned BEFORE July 15,2020 (or Oct 15, 2020 only if you filed an extension or filed your 2019 return before July 15.

After if you did not remove it in 2020 at all then you owe a 6% penalty for the 2019 tax year, AND because the penalty repeats every year until removed and it was not removed in 2020 before Dec 13, 2020, you also owe a 2020 6% penalty on the excess.

Before the end of 2021 yiu need to remove the excess, but nit the earnings as a regular Roth distribution that will get a 2021 1099-R with a coed J and will  not be taxable since yiu removed your own contribution.

At this date, there is no way to avoid both the 2019 and 2020 6% penalties since the time to remove has passed for both years.