In those counties with a population in excess of three hundred thousand (300,000) under the latest Federal Decennial Census, the county indigent defenders, for those counties subject to the provisions of Section 138.1a of this title, shall perfect appeals for those defendants which they represented in the trial court unless an appellate conflict exists between two or more such defendants, in which case the county indigent defender shall represent one defendant, the Oklahoma Indigent Defense System shall represent one defendant, and the court may assign the appeal of the case for any other defendants in the same manner as provided for conflict at the trial level in Section 138.7 of this title. If an appellate conflict of interest exists between the defendant and the county indigent defender in a case in which the defendant has received the death penalty, the district court may appoint the Indigent Defense System to represent the defendant on appeal. The Oklahoma Indigent Defense System shall also represent all indigent defendants from such counties who were not represented at trial by the county public defenders unless a conflict of interest on appeal exists between defendants, in which case the Oklahoma Indigent Defense System shall represent one defendant, the county indigent defender shall represent one defendant and the court may assign the appeal of the case for any other defendants in the same manner as provided for conflict at the trial level in Section 138.7 of this title.