If you filed the original tax return with TurboTax there is no additional charge to file a Form 1040X amended return.
Note that Form 1040X cannot be e-filed. You have to print it, sign it, and file it by mail. It takes the IRS up to 16 weeks to process an amended return.
Don't file the amended return until your first return has been accepted and you have received the original refund.
There may be a fee if the reason for the amendment requires an upgrade (such as adding as K-1 form).
Not sure about that comment - since the amended return needs to be mailed because of a K-1 form, why would there be a fee?
There is no fee to file an amend.
Amend for 2020 will not be available in TurboTax until late March. You do not amend until your original return has been processed. When you start your amend, TurboTax will show your refund amount as zero. Then that amount may change as you amend your entries.
When amend is ready, go into TurboTax and follow the instructions for amend. You will add your dependent in the federal section, then walk through all of the amend questions to be sure the information carries to the state. You will be amending both the federal and the state returns when you add a dependent.
You have 3 years from the date you filed your return or 2 years after you paid the tax due (whichever is later) to file an amendment.