The Supreme Court on Thursday denied a request from Edward Eugene Harper. Harper's conviction was upheld by the state Court of Appeals in March.
Harper was convicted in DeSoto Court in 2010 of conspiracy to commit sexual battery, child fondling and sexual battery. He was sentenced to 50 years in prison.
Harper was one of the FBI's "Ten Most Wanted Fugitives." He had evaded authorities since skipping a 1994 court hearing in DeSoto County.
The FBI says Harper was arrested in 2009 near his mountain camp in the Big Horn Mountains of Wyoming while he was tending sheep.