The Marvel Anime continuity for Japan is separate from the main Marvel continuity.
The project took top Marvel characters and reintroduced them for a Japanese audience via four 12-part series; Iron Man, Wolverine, X-Men, and Blade, which aired in Japan on Animax between October 2010 and September 2011. The announcement was confirmed at the 2009 San Diego Comic-Con. According to former Madhouse President and CEO Jungo Maruta, Marvel gave the anime studio free rein to re-imagine the Marvel superheroes for Japanese audiences. English version was premiered in the United States on G4. The series was guided by Warren Ellis. "It will create an entire parallel universe for Marvel," said Simon Philips, president of Marvel International about Marvel Anime.
An excerpt from X-Men:
Also, as starpilotsix pointed out, Spider-Man: India was originally published in India by Gotham Entertainment Group and tells the story of Pavitr Prabhakar in Earth-50101.
Pavitr Prabhakar, a simple Indian boy from a remote village, moves to Mumbai with his Aunt Maya and Uncle Bhim to study after getting half a scholarship. His parents died some years ago. Other students at his new school tease him and hit him for his studious nature and village background. He knows his Uncle Bhim is struggling to support him and his aunt Maya, and pay his school fees. Only Meera Jain, a popular girl from his school, befriends him. Meanwhile, a local crime lord named Nalin Oberoi uses an amulet to perform an ancient ritual in which he is possessed by a demon committed to opening a gate for other demons to invade Earth. While being chased by bullies, Pavitr Prabhakar encounters an ancient yogi who grants him the powers of a spider, in order to fight the evil that threatens the world. While discovering his powers, Pavitr Prabhakar refuses to help a woman being attacked by several men. He leaves the place, but comes back when he hears his uncle cry out, and discovers that he has been slain. He learns that Bhim was stabbed when he tried to help the woman. Pavitr Prabhakar understands that with great power comes great responsibility, and swears to use his powers for the good of others.
As it is officially part of the numbered Marvel universes and was involved in the Spider-Verse crossover, I think it's debatable as to whether it actually has a separate continuity, as compared the the Marvel Anime imprint, which seems completely separate.