Arkham State Hospital is a mental health facility located in Gotham City, which appears in the film Joker. In is the film's version of Arkham Asylum.
History
Arthur Fleck ( who's was once a patient at Arkham) visits the hospital to get records on his mother Penny Fleck and try and find out who his true father is. He steals a case file on his mother, and discovers that he was adopted, and that his adopted mother had allowed her boyfriend to abuse him when he was a small child, which had caused her to be incarcerated for a short while. The abuse is presumably what led to Arthur developing his disorder in which he can't stop himself laughing at stressful moments.
Arthur, now known as the criminal Joker, ends up incarcerated at Arkham State Hospital after being tied to multiple murders over the past few weeks, which led to riots breaking out in Gotham City against the rich. He presumably kills his psychologist during a session, and is pursued through the corridors of the hospital by the orderlies, much to his amusement.