A three-legged dog walks into a bar...

A three-legged dog walks into a bar and says, "I'm lookin' fer the man who shot my paw."

This is another "Walks into a bar" joke. The joke here is a pun, however in order to understand the joke the listener has to also recognize a common cowboy film trope in which a gunman is looking for the person that shot his father. In the imagined cowboy vernacular, "Pa" is often used to mean father, so "paw" is a pun on the word "Pa".