The Joker first appeared in 1940 in the first issue of Batman, illustrated by Bob Kane and written by Bill Finger. The two of them were the creative forces behind Batman’s stories and characters, not just Bob Kane who is always receiving the sole credit. Kane was usually responsible for the look and the feel, while Finger was taking care of the stories and origins.
Bob Kane: “I always felt rather badly that I never gave [Bill Finger] a byline. He was the unsung hero” (Batman: The Complete History)
Kane and Finger continued to develop Batman's universe until the 1960's with the help of other writers and artists, notably Jerry Robinson, who for years claimed that he was the one who invented Joker based on a Joker card and presented the idea to Kane and Finger.
Bob Kane: Bill Finger and I created the Joker. Bill was the writer. Jerry Robinson came to me with a playing card of the Joker. That's the way I sum it up. [The Joker] looks like Conrad Veidt — you know, the actor in The Man Who Laughs, [the 1928 movie based on the novel] by Victor Hugo. [...] Bill Finger had a book with a photograph of Conrad Veidt and showed it to me and said, 'Here's the Joker'. Jerry Robinson had absolutely nothing to do with it, but he'll always say he created it till he dies. He brought in a playing card, which we used for a couple of issues for him [the Joker] to use as his playing card - May 17, 1994, Entertainment Weekly Interview