Representative Barry Moore, an early backer of the president during his first campaign, faces Jared Hudson, a former Navy SEAL tapping into the excitement for outsiders.

© Michael Brochstein/Sipa USA, via Associated Press; Mike Stewart/Associated Press

Mr. Trump backed Mr. Collins over Derek Dooley, a former football coach supported by Gov. Brian Kemp, a Republican whose relationship with the president is strained.

© Audra Melton for The New York Times