for 2023 we paid federal taxes; after filing an amended return we will actually receive a refund; how do we receive the funds we paid last year by mistake?

I think you are saying that when you originally filed your 2023 tax return, it showed a balance due, which you paid.  You later filed an amended tax return which shows that you are due a refund.  In addition to the refund, you want to know how to back the amount you paid with the original tax return.  If that is what you are asking, the answer is that the amount you overpaid with the original return would have been factored into calculating any refund you are due from the amended return, if the amended return was completed correctly.  If  your amended return did not reflect the amount paid with the original return, the IRS will correct it, adjust your account and refund the total amount of your 2023 over payment.  You cannot claim a refund due from a prior year on your current year tax return.  I didn't understand your question correctly, you'll need to clarify what you actually did.