As of this writing, there have only been a handful of Asian superheroes who have had their own series. The first was in 1973 and then there was a big gap until the 21st century, with most being written in the last few yars.
Amadeus Cho (Totally Awesome Hulk) — Korean-American
Winner of the "young genius" contest who used nanites to remove the Hulk from Bruce Banner and place it in his own body,
Solo series since 2016
Cindy Moon (Silk) — Asian (probably Korean)-American
Bit by the same radioactive spider that gave Peter Parker his super powers, making her have the same powers as Spider-Man.
Solo series in 2015
Daken (Dark Wolverine) — Half-Japanese
The son of Wolverine and his Japanese wife, who has much the same powers.
Solo series 2010-2012
Jubilee (X-Men member) — Chinese-American
A mutant with the ability to create energy plasmoids from her hands (and as of 2010, she's lost her mutant powers and is now a vampire. Comics are weird).
Solo series 2004-2005
Kamala Khan (Ms. Marvel) — Pakistani-American
A Muslim girl and an Inhuman with the ability to stretch her body.
Solo series since 2014
Shang-Shi (Master of Kung fu) — Chinese
A martial-artist and the Son of Fu Manchu.
Solo series 1974-1983
Of the other Asian Marvel characters, if they are not a supervillain, they tend to be a member of the X-Men.
The closest we have got to a headlining Asian superhero in the Marvel movies is Yukio, who teams up with Logan in The Wolverine and has the power to forsee death. It's not part of the Marvel Cinematic Universe, but it is part of the X-Men universe.