No, TurboTax does not currently charge a fee to file amended tax returns. However, TurboTax would charge a fee if it was determined that the reason you needed to file amended tax returns was a situation that required a product upgrade, i.e. Free Edition to Deluxe, etc.
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Please see the following TurboTax FAQ for instructions on how to amend your tax return:
https://ttlc.intuit.com/replies/3288565