How do I amend my return when I forgot to claim unemployment on my return? Or can I claim it on my next years return?

[Sepeda92]

2020 tax return

[DoninGA]

Once a tax return has been filed it cannot be changed, canceled or retrieved

You will have to wait for the IRS to start accepting or rejecting 2020 tax return on February 12, 2021
If the return is rejected you can make the necessary changes and e-file again.
If the return is accepted you will have to amend your original tax return. An amended return, Form 1040X, can only be printed and mailed to the IRS, it cannot be e-filed. The IRS will take up to 16 weeks or longer to process an amended tax return.

Before starting to amend the tax return, wait for the tax refund to be received or the taxes due to be paid and processed by the IRS.

See this TurboTax support FAQ on amending a tax return originally completed and filed using the 2020 TurboTax online editions - https://ttlc.intuit.com/community/amending/help/how-do-i-amend-my-turbotax-online-return/01/27577

[SweetieJean]

No, you cannot wait to claim it next year.  However, the IRS gets a copy of the 1099-G from the state's unemployment bureau, so might make an adjustment automatically.

[Sepeda92]

Great thank you!