Knott County Judge Executive Randy Thompson and three others are scheduled to appear in federal court this month.
The Hazard Herald reports they want their 2008 convictions overturned.
Thompson, along with John Mac Combs, Phillip Champion, and Ronnie Adams allegedly allowed county blacktop and gravel be applied to private drives in exchange for votes leading up to the 2006 general election.
All of the men remain free as the appeals process continues.
Attorneys will present their arguments July 27th before the U.S. Sixth Circuit Court of Appeals in Cincinnati.