25-10-503. How costs on appeal claimed. Whenever costs are awarded to a party by an appellate court, if the party claims the costs, the party shall, within 30 days after the remittitur is filed with the clerk in the original proceeding, deliver to the clerk a memorandum of the party's costs, verified as prescribed in 25-10-501, and then the party may have an execution for the costs as upon a judgment.