Martha Wayne (Flashpoint)

The Joker (real name: Martha Wayne) was a supervillain in the Flashpoint timeline, who often operated with an MO relating to comedy-related crimes.

Biography
She had initially been Martha Wayne, the mother of Bruce Wayne, who would have become Batman. Unfortunately, a twist of fate occurred after Barry Allen, aka, the Flash, changed the timestream, which resulted in she and her husband Thomas Wayne surviving Joe Chill's fateful ambush, but their son dying as a result. This ultimately broke her, driving her completely insane from grief and having her adopt the identity of the Joker, as well as committing various crimes in Gotham, and also resulting in Thomas in becoming a violent vigilante known as Batman in an attempt to stop her.

By the time of the Flashpoint arc, she had kidnapped the twin sons of Harvey Dent without leaving a ransom. She then, at her hideout of Wayne Manor, manipulated Commissioner Gordon into shooting the daughter by dressing her up in a Joker outfit, and then murdered the son and then Gordon. Eventually, Batman arrived, and she proceeded to bludgeon her former husband with a hammer, an action Batman willingly endured for a chance at getting a glimpse of the remaining psyche of his former wife. Ultimately, he managed to temporarily get through to her, and revealed that they may have a chance of undoing the events that happened, although it may result in their deaths, Martha accepted, although upon learning what will become of Bruce (that he'll become Batman, like his father), she goes insane again and commits suicide.

Trivia

 * Martha Wayne's Joker appearance had an uncanny resemblance to The Dark Knight version of the Joker.
 * On a related note, this version alongside the Nolanverse Joker are the only Joker incarnations who hadn't been dunked into a chemical vat beforehand as part of their becoming the Clown Prince of Crime.
 * This is one of only four Joker characters to have a definitive backstory beyond encountering Batman, the only others being the version from the 1989 Batman film played by Jack Nicholson, Joker (Arkhamverse) from the Arkham  games, and the version from the DC Animated Universe (although one can argue due to the flashbacks in Batman: Under the Red Hood and the animated adaptation of Batman: The Killing Joke that both versions of the Joker may have had backstory beyond encountering Batman).
 * Ironically, this is also the only version of the Joker whose origin story stemmed from the exact same event as Batman's origin story (in this case, the death of Bruce Wayne)
 * This is one of only two villainous Joker incarnations to be female instead of male, the only other being Bianca Steeplechase.
 * The second Joker incarnation whose name is known, with the first being Jack Nicholson's Joker in Tim Burton's 1989 film Batman.
 * This is also one of the few Joker incarnations to be portrayed as a truly sympathetic character, with another being the version from the animated adaptation of Batman: The Killing Joke.