Mark tries to set Lucas up with a pretty young woman he thinks would make a perfect wife for his Pa. Lucas soon finds himself contending with the two brothers of this young woman as well as some outlaws bent on killing him.
From "The Rifleman Episode Guide"
The strength of tele-genetics is not always a given; just because two characters look alike (due to the real world splainin of the same actor playing both roles), that doesn't mean that they have to be related.
I stated in a post a few days ago that Little Joe Cartwright and Will Fulton/Billy Mathis were father and son (although they never knew it), but that doesn't mean Hoss had to be the father of Peter Snipe from this episode of 'The Rifleman', even though Dan Blocker played both roles.
But Peter Snipe and Hoss Cartwright still could have been related. It's always pozz'ble, just pozz'ble, that the mother of Joshua, Rebecca, and Rhoda Snipe might have cheated on her husband with Gunnar Borgstrom, the brother of Ben Cartwright's second wife (as seen in the 'Bonanza' episode "The Last Viking".)
Also, Joshua Snipe may have gone on to become a Jesse James impersonator - not for any Wild West show, but to pursue a criminal career. (Why? Because that Jesse James who encountered the Martian Exigius 12½ in an episode of 'My Favorite Martian' in no way could have been the real deal! Especially since he was older than his "brother" Frank, also an imposter, when it should have been the other way around.)