The plot could develop with Harry being abandoned in a big Japanese city like Tokyo. He might end up in the muggle part of the city at first and have to use his wits to get by. Eventually, he attracts the attention of Japanese wizards who are both curious and cautious about him. They take him to their magical enclaves where he discovers that there are different types of magic in Japan. There could be political intrigue within the Japanese wizarding community regarding Harry, with some seeing him as a threat and others as an opportunity. He has to navigate through all this while also dealing with his own feelings of abandonment.
She could face a lot of challenges. For one, the language barrier would be difficult. She'd have to learn Japanese to communicate and study in the new magical environment. Also, the Japanese magical society might have different views on her status as an outsider, and she might have to prove herself worthy to be part of their community. However, she is Harry Potter after all, so she would likely adapt and grow in this new setting.
One interesting fanfiction could be where Harry Potter is abandoned in a small Japanese village. He might discover the local magical traditions that are different from the British ones. Maybe he meets a kind Japanese wizard family who takes him in and he has to adapt to their way of life, like learning about Japanese magical creatures and spells.
He'd probably be more reserved and polite, as those are common traits in Japanese culture. His sense of honor might be more in line with the Japanese concept of 'bushido'.
Well, her Hogwarts - centered story would completely shift. Instead of going through the trials at Hogwarts, she'd be dealing with the Japanese magical schools or training systems. Maybe she'd end up in a school like Mahoutokoro, where she'd have to learn different magical techniques and rules.
The plot could develop with Harry trying new magical sports or activities. For example, he might discover a new form of broomstick racing that's more dangerous and exciting.
One possibility could be that Harry discovers his connection to Artemis in a very unexpected way. Maybe he starts having strange dreams or visions that lead him to ancient artifacts related to Artemis. As an 'abandoned son', he might face a lot of internal conflict about his identity and where he belongs. He could also inherit some unique powers from Artemis that set him apart from other wizards.
The plot could start with Harry being born on a spaceship or a space colony. As he grows, he discovers his magical powers, which are different from those on Earth. He then gets a message or a sign that leads him to a quest. This quest might involve finding a lost magical object that has the power to save the space - wizarding community from a dark force. Along the way, he meets other magical beings from different parts of space and they form a team to complete the mission.
In this fanfiction's plot, Harry's identity as the Boy Who Lived would be intertwined with his military upbringing. He could start a sort of 'wizarding army' within Hogwarts, recruiting students who are willing to fight against the dark forces. His training by soldiers would make him a natural leader in this regard. The story would then revolve around his efforts to build this army, face the opposition from some traditional wizards, and ultimately use this new force to defeat Voldemort in a more strategic and coordinated way.
A really interesting plot development could be the connection between Loki's magic and the magic of the wizarding world. Harry could start to experiment with combining the two types of magic. For example, she might use Loki's magic of deception to create false horcruxes to mislead Voldemort. This could lead to a complex web of intrigue as Voldemort tries to figure out which are the real horcruxes and which are the fakes. At the same time, Harry could be exploring her relationship with her father through memories or encounters with Loki's essence, which would add a whole new emotional and character - driven aspect to the story.
The plot could start with Harry being found by a samurai clan. He'd grow up learning their ways. Then, when he discovers his magical heritage, he has to blend the two worlds. Maybe he uses samurai skills to fight dark wizards.