Notwithstanding the provisions of § 16.1-135, any person convicted in a general district court, a juvenile and domestic relations district court, or a court of limited jurisdiction of an offense not felonious may, at any time before the appeal is heard, withdraw an appeal which has been noted, pay the fine and costs to such court, and serve any sentence which has been imposed. A person withdrawing an appeal shall give written notice of withdrawal to the court and counsel for the prosecution prior to the hearing date of the appeal. If the appeal is withdrawn more than ten days after conviction, the circuit court shall forthwith enter an order affirming the judgment of the lower court and the clerk shall tax the costs as provided by statute. Fines and costs shall be collected by the circuit court, and all papers shall be retained in the circuit court clerk’s office. Where the withdrawal is within ten days after conviction, no additional costs shall be charged, and the judgment of the lower court shall be imposed without further action of the circuit court.