What 1950s era movie starred John Wayne as a hillbilly by the name of Young Matt?

There is no 1950s era movie starring John Wayne as a hillbilly named Young Matt. John Wayne did star in a number of Western films during the 1950s, but none feature a character with that name. It is possible that you are misremembering the movie or the character.

Do you recall any other details about the movie, such as the plot, other actors, or the setting? This information might help me identify the film you're thinking of.