The economic impact checks received this summer will not count as income and they will not be taxed by state or federal governments.
They will not reduce your refund or increase the amount you owe on 2020 taxes.
You will need to report it on your 2020 taxes.
In fact, the impact payment will not even count as income for qualifying or eligibility for federal assistance of benefit programs.
If you made too much money in 2019 to qualify for an impact check in 2020, but your 2020 income dropped and now you would qualify, you can take the impact payment as a tax credit in 2020.
In some situations, when you file your 2020 income tax, you will get more of a credit than you got in your impact check. For example, suppose in 2019 you did not have a child. Now suppose in 2020 you did have a child. You would not have received a $500 credit for your child on your impact check. But when you do your taxes for 2020, you will receive the $500 credit and it will reduce your tax bill dollar for dollar.
While the impact check will not be taxed, unemployment benefits will.