This is a story idee that's been stuck in my head ever since I watched the movie.
So the basic idee of this story is that Carol Danvers(Captain marvel) is the mother of Shirou. She met his father about 2 years(optional) before she lost her memory and joined the Kree. Shirou's dad also past away (how is up to you).
This story has to take place after the Captain Marvel movie and the 5th Holy Grail war.
The story can take place in any fate route (personally I favour the Avalon pairing, but if you want to use UBW or HF that's up to you).
Some optional things:
Carol returns to earth after 18 years, 10/12 years after the movie(2005/2008)
Her friend Maria tells her about Shirou. Carol then goes to Fury, who is now the the director of SHIELD, who gives her more info about her son.
So that's the basic outline of the story, the rest is up to you. I'm not that good of a writer and I want to see other peoples take on this Idee.
Good Luck!!