Pattycake was a child's game in which two participants would clap each other's hands together while being accompanied by a nursery rhyme.
In 2268, while talking to Leonard McCoy and Bela Okmyx about Jojo Krako, Captain James T. Kirk said to them, "I'm getting tired of playing pattycake with you penny-ante operators." It was his way of saying he was done playing games and wanted to get serious. (TOS: "A Piece of the Action")