She could be a completely ordinary girl from the wizarding world, but with a heart of gold. Harry sees something in her that reminds him of himself when he was young. So, he decides to adopt her and give her a better life. Maybe she has a love for animals like Hagrid, and that's one of the things that endears her to Harry.
The girl might be a descendant of an old wizarding family that has fallen on hard times. Harry adopts her to revive the family's honor. She could have some special knowledge or heirloom that attracts Harry's attention and makes him decide to take her in.
She could be a young girl who has lost her parents in a magical accident. Maybe she has some special powers that Harry notices and that's why he decides to adopt her.
Perhaps the girl is a huge fan of Harry Potter in the fanfiction world. When Harry discovers her, she's being bullied for her love of him and his story. So, he adopts her to protect her. He then shows her the real Hogwarts, not just the one she's read about. Along the way, they might face challenges from those who don't like the idea of Harry having an adopted daughter, but they overcome them together.
One possible plot is that the girl is from a non - magical family but has a deep fascination with Harry's story. Harry discovers her and decides to adopt her as she has a natural inclination towards magic. He trains her privately at first, and as she gets better, he reveals her to the wizarding community. Along the way, they face some challenges from those who are against a Muggle - born being trained by Harry, but they overcome them together.
She could be a descendant of one of Fry's friends in a really convoluted time - travel related scenario. Maybe she's related to Bender somehow, and that's part of the reason Fry feels obligated to take her in.
It could be Ginny Weasley. Since they have a relationship in the original series, it's not too far - fetched to imagine a scenario where she gets pregnant. Maybe they got carried away during a time of peace in the wizarding world.
It could be a young wizard who lost their parents during the final battle against Voldemort. Harry feels responsible for all the orphans created by the war and decides to take this particular child under his wing.
The Shafiq girl could be a transfer student from another wizarding school. She comes from a family with a long history in the wizarding world but has a different upbringing. This gives her a unique perspective when she enters Hogwarts and meets Harry Potter. She might bring with her new magical techniques or knowledge that catches Harry's attention.
The kid could be a lost descendant of one of the old wizarding families. Maybe a long - lost relative of the Weasleys or the Blacks. Harry discovers this connection and decides to adopt the kid to preserve the family's legacy.
I think a younger version of Fleur Delacour could be an interesting character for a younger girl in the fanfiction. Fleur was very confident, beautiful, and had a certain elegance about her. A younger girl modeled after her could bring a different kind of charm to the story. Or the girl could be a new character altogether, perhaps a young witch from a far - off land who has her own set of magical skills and a curious nature, which would make her a great addition to the Harry Potter world in the fanfiction.
She might be an old friend of Harry's from his childhood in the Muggle world that he didn't know was a witch. She had been suppressing her magic for a long time and fainted when it finally burst out uncontrollably. Harry wakes her up and helps her understand and control her new - found powers.