Perhaps the child is a half - elf. In the wizarding world, half - elves often face discrimination. Harry and Hermione, being the kind - hearted people they are, might decide to adopt a half - elf child. They would then have to deal with the unique challenges that come with raising a half - elf, such as the child's connection to the elf community and the prejudices they might face from other wizards.
The adopted child could be a muggle - born with a great potential for magic. Maybe their parents were killed by dark wizards who were against muggles in the wizarding world. Harry and Hermione, having both experienced prejudice, would be determined to give this child a chance.
Well, perhaps in the fanfiction, Harry and Hermione find a child who has special needs in terms of magic. For example, the child has an uncontrollable magical power that scares other families away. But Harry and Hermione see the potential in the child. They start to work together, with Hermione using her vast knowledge of magic and Harry using his own experiences, to help the child learn to control their power. As they do this, they form a very close family unit.
It could be a child of a minor god who has been overlooked. Maybe the child of Hecate, a young demigod with some really interesting magic powers that Percy and Artemis see potential in.
Perhaps the child is the offspring of a Titan. This would make for an interesting story as Percy would have to deal with the potential danger and mistrust from other demigods. But Percy, being Percy, would see the good in the child and adopt them regardless. The child might have unique powers that set them apart from other demigods, like the ability to control time or space.
Their child might be extremely intelligent, inheriting Hermione's sharp mind. He or she could also have a brave heart like Harry. Maybe the child would be a natural at magic, quickly mastering spells and showing great potential at Hogwarts.
Obviously, their child is a very popular character. But also, the friends of their child at Hogwarts, like a new generation of Gryffindors or other house students. There could be a character who is a descendant of an old wizarding family that has a special bond with Harry and Hermione's child.
There could also be new dark wizards or witches who envy the power and fame that Harry and Hermione have. They might see the child as a way to get to Harry and Hermione, or they might simply want to prove themselves by challenging the family. For example, a dark wizard who has developed a new and dangerous form of dark magic and wants to test it on the child.
There could be a new dark wizard or witch emerging. This character could be jealous of Harry and Hermione's influence and see the baby as a way to get to them. They might try to harm the baby or turn it against Harry and Hermione, creating a lot of conflict and danger in the story.
Perhaps in the fanfiction, Harry and Hermione raise a child who has a connection to a long - forgotten dark magic. They have to protect the child from those who would use the child's power for evil. Along the way, they face challenges in the wizarding world where some people are suspicious of their decision to raise this special child. But they stand strong, using their combined knowledge and skills to keep the child safe and raise it with good values.
One possibility is that the story could revolve around the challenges they face as parents in the wizarding world. Since they are both well - known figures, their child might be under a lot of public scrutiny. The child could also have to deal with the legacy of Voldemort, even though he's been defeated, as there could still be remnants of his followers causing trouble.
They might face challenges in the child's education. In the ninja world, there are specific skills and knowledge that the child needs to learn. Naruto and Hinata have different fighting styles and abilities. Deciding which ones to teach the child first could be a headache. Also, the child might struggle with making friends in the village. Naruto was an outcast as a child, and they'd want to prevent the same for their adopted child. They'd need to be very involved in the child's social life to make sure he or she is accepted.