The use of the term "red herring" has its history from the 1800s as a smoked "red herring" was dragged across a game trail to throw hunting dogs off the scent.
Only the best hunting dogs were able to discern the differences and continue to pursue the game.
The phrase "red herring" came into popular use in literature with detective stories, crime novels etc...as it was a trick used by a villian to throw the cops off the chase.
A red herring is a phrase given to any attempt to send someone off on the wrong direction as they pursue some item of information. So, if you think about literary examples of red herrings, detective fiction is going to be full of red herrings, because a good author will deliberately make you think that the murderer is someone else from who it actually is. It wouldn't be a good book otherwise!
If you want a more "literary" example, you might want to think about Great Expectations by Charles Dickens and how Dickens very carefully plants a red herring in that story. When Pip discovers he has a mysterious benefactor, we and he automatically thinks that it is Miss Havisham, and we never suspect it might actually be the escaped convict Magwitch.