Mewthree is a Pokémon which has never appeared in any game or anime episode, though it has had one appearance in the overall Pokémon franchise. It is the second clone of Mew. It is technically not a real Pokémon, as it is just a transformed form of Red's Clefairy.
Mention in the anime
After successfully cloning Mew and creating Mewtwo, one of the scientists exclaims that they should "get started on Mewthree".
Appearances in the manga
Pokémon Pocket Monsters Manga
In the Pocket Monsters manga, in Mewthree's only appearance to date, Red's Clefairy becomes Mewthree after merging its own DNA with that of Mewtwo's. Clefairy/Mewthree proceeds to battle and defeat Mewtwo before being reverted to normal.