This is a great question. The Klu Klux Klan makes an appearance in chapter 15 in the a conversation between Jem and Atticus.
Jem is frightened as the case is about to start. He is afraid that someone might seek to harm Atticus. More specifically, he is afraid that the Klu Klux Klan will come to Maycomb and start causing trouble.
Atticus dismisses this idea as impossible. The Klu Klux Klan, according to Atticus, has been gone for a long time. Here is the dialogue:
Atticus lowered the paper and gazed at Jem. “What have you been reading?” he asked. Then he said gently, “No son, those were our friends.”
“It wasn’t a—a gang?” Jem was looking from the corners of his eyes.
Atticus tried to stifle a smile but didn’t make it. “No, we don’t have mobs and that nonsense in Maycomb. I’ve never heard of a gang in Maycomb.”
“Ku Klux got after some Catholics one time.”
“Never heard of any Catholics in Maycomb either,” said Atticus, “you’re confusing that with something else. Way back about nineteen-twenty there was a Klan, but it was a political organization more than anything. Besides, they couldn’t find anybody to scare.
All seems well after Atticus says these words, but the context leaves the reader feeling uneasy. The ominous tone is confirmed when Atticus goes to the jail to make sure all is well with Tom Robinson. This is when Mr. Cunningham and a mob come to harm Tom Robinson and even Atticus. So, the idea or the spirit of the Klu Klux Klan is very much present. In this way, the Klu Klux Klan develops the idea of mob violence and racism.