The Red Ryder BB gun is a BB gun made by Daisy Outdoor Products and introduced in 1938 that resembles the Winchester rifle of Western movies. Named for the comic strip cowboy character Red Ryder, it is arguably the most famous BB gun in American history.
Found at the "Bob's Pre-owned Car Mart" special random encounter, along with some BBs and a normal BB gun. Look in the boxes behind the locked door. Very rare to get in the first game. This encounter is a reference to an event in Wasteland.
The Red Ryder BB gun appeared in the 1983 film A Christmas Story, where the main character, Ralph, wants a Red Ryder BB gun for Christmas, but is ridiculed by adults that say, "You'll shoot your eye out.".
The Red Ryder BB gun was also a powerful weapon obtainable in Wasteland, the predecessor game to the Fallout series. In Highpool, the party has to fight the child whose dog (Rex) "was gunned down by vigilante Rangers," or it could be acquired via cheat.
The Red Ryder himself is another reference to the BB gun and Wasteland, he shows up to fight the Rangers in revenge should they murder the children making fun of them after falling into the river.