If you made a mistake and claimed the 3rd stimulus payment, do not file an amendment until you know the original return has been received and processed. The IRS will most likely catch this error before issuing you a refund and send you a letter. If you know you owe, you could make the payment to avoid any penalty or interest being imposed.
If by chance you receive the refund from your original return, then you can prepare the amendment and send the payment with the amendment. If you go ahead and make a payment then show the payment made on the amended return.
