This guy was called "Gaggy", and he was more or less the Joker's Jester. His job was to make the Joker laugh. Although he also helped the Joker fight Batman.
I thought this guy was Moe Howard. Look at the hair.
He also looks kind of like Moe otherwise, and tends to act pugnacious in spite of his small size. While he doesn't poke anyone in the eyes as Moe did, he does hold his hands over Batman's eyes with the idea that the Joker can then punch Batman, something that was represented on the cover. The trouble is, Batman ducks, and then the Joker just punches Gaggy instead.
Batman beat the Joker, the same as he had without the involvement of the Joker's new partner.
And Gaggy the Joker Stooge didn't live happily ever after.
During the course of the story, Gaggy uses a recognizable Moe Howard line. He says "Why you--!" on page 9. In the original Three Stooges films Moe would frequently say that in reaction to the knuckleheaded stupidity of some of the other characters, frequently responding with violence as well.
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Moe Howard's autobiography, previously published as MOE HOWARD AND THE THREE STOOGES, has come out in a new edition with the original title, I STOOGED TO CONQUER.