After losing at the trial level, the Houston brothers are seeking relief in the U.S. Court of Appeals for the 6th Circuit, where their federal convictions are being challenged.
Leon Houston, 55, was convicted in November 2013 for using a telephone communication to threaten to kill Cleveland attorney James Logan.
U.S. District Judge Danny Reeves sentenced him to the maximum five years in March.
The 6th Circuit covers Kentucky, Michigan, Ohio and Tennessee.
The U.S. Attorney’s Office must file a brief in the case by Dec. 22.