Any person who shall have been convicted of a criminal offense against the laws of this state, by the judgment of a justice court, or by a municipal court for the violation of an ordinance of the municipality, who by reason of his poverty is not able to give bond as prescribed in Section 99-35-3, may nevertheless appeal from such conviction on his making an affidavit that, by reason of his poverty, he is unable to give bond or other security to obtain such appeal, but the appeal in such case shall not operate as a supersedeas of the judgment, nor discharge the appellant from custody, but the judgment shall be executed as if an appeal had not been taken, unless the presiding judge of the appellate court shall, for good reason, see fit to stay the execution of the judgment rendered by the court below by ordering the release of the defendant on his own recognizance, and this shall not affect the trial of the case anew in the appellate court.