The story of how the joker got his scars
There are several versions of the Joker scars story in The Dark Knight and You Know How I Got These Scars: How the Joker Writes His Own.
In the movie, the conflicting stories about his past are there on purpose to another if I'm going to have a past, I prefer it to be multiple choice!.
The First Story
There is no true origin of the Joker in any media.
Description:The second version he tells to Rachel: His technical genius is not limited by practicality, allowing him to hijack Gotham's television airwaves to issue threats, transform buildings into death traps, launch a gas attack on the city and rain poisoned glass shards on its citizens from an airship. When the Joker escapes, he attacks the Black Glove, burying its leader Simon Hurt alive after the supervillain considers him a failure as an opponent; the Joker is then defeated by the recently returned Batman. He wanted an exotic, enduring character as an ongoing source of conflict for Batman similar to the relationship between Sherlock Holmes and Professor Moriarty , designing a diabolically sinister-but-clownish villain. Apparently Jerry Robinson or Bob, I don't recall who, looked at the card and they had an idea for a character