Perhaps it's a story full of his own made - up characters. He might create a story about a superhero version of himself who saves the day in the most absurd ways. For example, he could use his love for beer as a superpower to defeat an evil villain who wants to ban all fatty foods in Quahog.
The neighbors could be in the story too. Quagmire, for instance. Peter might tell a story about how Quagmire got into a really embarrassing situation and how they all helped him out (or made it worse). Or he could include Cleveland and tell a story about a neighborhood barbecue gone wrong because of something Cleveland did.
Well, it could be the ones that are full of humor and family - related themes. Maybe the stories that involve the Griffins' own family adventures and the crazy things they do, which he then relates to the characters in the books he tells about.
One Peter Griffin scary story could be about him getting lost in a haunted forest near Quahog. He hears strange noises, like the howling of a creature that doesn't seem to be from this world. As he wanders deeper, the trees seem to close in on him. He starts to see shadowy figures that disappear when he looks directly at them. He tries to run but keeps getting turned around, and every step seems to take him further into the unknown.
It depends on the day. Sometimes Stewie might be in a bad mood and not be as receptive, but on most days, he likely enjoys the special time with Peter and the stories he tells.
The unexpected twists. For example, if Peter, who is usually a bumbling but loveable character, suddenly becomes the target of a supernatural force that he can't understand. It's interesting because it goes against his usual comical role.
I'm not entirely sure which specific 'Peter Griffin Never Ending Story' you are referring to. It could potentially be a fan - made or very niche story related to Peter Griffin from 'Family Guy'. Maybe it's a creative exploration of his character in an ongoing, never - ending narrative.