A Case Closed Fan Fic by Magic Conan 14 that can be read here. It was first published in 2011, and is of the mystery/fantasy genre.
Conan, Ai, Heiji and Kaito receive invitations to a school named after its principal, Artemis Kuroshi. As the name of the fic says, the Artemis Kuroshi school is no ordinary school...the four discover that they are reincarnations of the Magic League - a band of thieves that have some connection to Artemis. Not only that, but they discover that the powers the Magic League possessed were transferred to them...except Heiji, who receives a different power entirely. Erika, roommate of Ai, ends up dead. The rest of the fic is all about the team - Renegade - tracking down the killer, Case Closed style, with the help of Ai's other roommate Gloria.
It's the second of a trilogy: the second is this one, the last is Intertwined and the first (a prequel named Winged and Dangerous) was never released online. Vault explains some of the backstory of the characters. Unfortunately, the author decided to tie off the ends and not release Intertwined after a while.
The Mysterious School contains examples of:
- Academy of Adventure: The Artemis Kuroshi School is indeed one.
- An Ice Person: Haibara Ai.
- Big Bad: Artemis Kuroshi.
- Back from the Dead: Shinichi says this as a bit of a joke:Shinichi (as the Sparkling Baron): Persephone! I'm back from the dead!
- Casting a Shadow: Shinichi/Conan, by means of the attack Moon Wing.
- Elevator School: If a school can manage to have Kaito (16 - 17 years old) and Conan (6 - 7 years old) together in a school, then it's obviously one.
- Extranormal Institute: The Artemis Kuroshi School.
- Extra-ore-dinary: Conan/Shinichi.
- Great Detective: Well, it's a Case Closed fic after all...it was bound to pop up somewhere, right?
- Legacy Character: All four of Renegade. (Actually three because Kaito's already the Kaito Kid.)
- Personality Powers: Conan is the one who can keep calm in most situations. Haibara has a Sugar-and-Ice Personality. Heiji has a short temper and a lot of impulsiveness (for a detective, at least). Kaito is the trickster of the group.
- Playing with Fire: Heiji. (Also Natsu, although he never does use his powers in the fic. See Shout-Out for more details.)
- Psychic Powers: Gloria.
- Reincarnation
- Sacrificial Lamb: Erika Beruteu.
- Shock and Awe: Kaito.
- Shout-Out: To Fairy Tail via Natsu appearing midfic.
- Somewhere in there is one to Real Life, as a thanks to someone named Anita.
- Stranger in a Strange School: Not one, four.