I believe the Killing Joke did address his supposed backstory, but he was the one telling it. Like with Ledger's Joker and his multiple backstories, he could have made it up. I don't think there's an official backstory. But I'm not a comic book aficionado, so I obviously defer to the more knowledgeable on this.

The other characters have better backstories. For instance, Mr. Freeze started as a champion Austrian bodybuilder with a penchant for cheesy one liners and political aspirations. After marrying into the local royal family, he became governor of California and was brought low only by the erotic ministrations of a hulking chamber maid. Frozen out of polite society, film and family, he began making low budget action films and trying anything he could get his hands on to remain youthful...enter a toxic mix of dysfunctional cryotherapy chamber, statins and a near fatal dose of icy-hot.