His attorneys argued Friday in Chicago before the 7th U.S. Circuit court of appeals after an order from the nation's high court.
The former Republican governor is nearing the end of a six-and half-year federal prison sentence on several corruption charges.
Attorneys say there's no evidence Ryan took bribes. They say the court should overturn those convictions based on a 2010 Supreme Court ruling curtailing "honest services" laws.
Federal prosecutors disagreed.