Siblings In Everything But Blood
She first saw him when she was 22 years old, and injured on a mission. He was 10 years old, and visiting an aquarium. Percy Jackson looked into Natasha Romanoff's weary but determined eyes, and decided to help her. And so, he pulled a lever, spilling his class and her enemies into a tank. That was not the last she saw of him.
By the time several years pass, the two green-eyed siblings by bond will be known as heroes, albeit of different worlds. Perhaps they don't know everything about each other. But they do know that they will always have each other's backs.
He helps her out when her missions don't go the way they planned, which doesn't happen too often.
She teaches him how to be a good spy, although that isn't the intention when they start the lessons.
And they become very close, just as close as true siblings, in fact.
So when Natasha finds herself in a complicated position during the Avengers' Civil War, Percy decides to interfere. And the Avengers are extremely surprised when they meet Natasha's younger brother. Plans are made and set in motion, alliances are completely misconstrued, friendships are tested and broken, and the two siblings find themselves on their own side against the world.
However, there's something bigger in the works for the Avengers, and they'll need all the help they can get to face it. Including the two green-eyed siblings in everything but blood.
This is largely Marvel canon compliant up until Captain America: Civil War, with Percy's interaction with Natasha being a background to the PJO books.