Edwards, a former Marine, ran his own ranching business for 30 years in Canadian County before joining the sheriff's office as a deputy.
In Logan County, incumbent Sheriff James Bauman is running against Ben McHand.
Bauman, a Republican, was elected in 2008 after defeating former sheriff Randy Richardson.
McHand, a Democrat, is retired from the Oklahoma Highway Patrol, according to his Facebook page.
Former Edmond resident Ryan Lake, a Republican, is running for sheriff in McClain County.
Lake is running against incumbent Sheriff Don Hewitt, a Democrat, who has been the county's top lawman since 1999.
In Lincoln County, incumbent Sheriff Charlie Dougherty, a Democrat, is facing off against Wesley Scott Donovan.
Dougherty has been sheriff since 2010. His challenger, a Republican, is a former police chief in Carney and helped train police officers in Iraq and Afghanistan.
In other races
Three other Oklahoma County races already have been decided: Carolynn Caudill, the incumbent county clerk, ran unopposed in her re-election bid; Brian Maughan, the incumbent District 2 commissioner, won re-election in a July primary; and Tim Rhodes, the current deputy county court clerk, won a runoff election in August to take over a vacant seat for county court clerk.
CONTRIBUTING: Zeke Campfield, staff writer