One possibility is that Harry would use this opportunity to change certain events in the past that had a negative impact on the baby or its family. He could also form a special bond with the baby. Maybe he'd introduce the baby to some of his friends from his own time who are also in the past now. This could create a whole new set of relationships and storylines in the fanfiction.
Well, it could be a really interesting story. Snape, being the one to adopt Harry, would have to deal with his own complex feelings towards James Potter while raising Harry. He might initially be strict, but gradually, as he sees Harry's own personality develop, he'd grow to have a very deep and loving bond with him. He could also introduce Harry to a different side of the wizarding world, one that is more influenced by his own Slytherin roots.
Definitely his professors when they were younger. For example, Snape as a student. This would be a strange interaction considering their relationship in Harry's own time. He could also meet Hagrid when he was just starting out at Hogwarts. And there's a good chance he'd run into Sirius and Remus during their school days, and perhaps form new friendships or alliances with them in the past.
In a fanfiction where Harry Potter is on Asgard, he would face many challenges. His magic might not work in the same way as it does on Earth. He'd need to adapt quickly. He could also be seen as a threat by some Asgardians. However, his courage and quick thinking, which he developed in his battles against Voldemort, would help him survive. He might even teach the Asgardians some things about the power of love and friendship, which are important in the wizarding world.
One possibility is that they would try to find the origin of Voldemort's power in the past. They could search for the early Horcruxes or try to stop Voldemort from making them in the first place. Also, their presence in the past might cause some confusion among the wizards of that time. Some might think they are some kind of time - traveling wizards with strange powers. But overall, it would be a very exciting adventure full of unpredictable things.
Well, it could be that the baby dragon has some special powers. Maybe it can communicate with Harry telepathically. This would lead to some really interesting adventures as they bond and learn from each other.
Well, Harry might use his magic to make the baby laugh. For example, he could turn the baby's rattle into a little magical creature that dances around. He'd probably also be very protective, like how he was with his friends at Hogwarts.
In this fanfiction, perhaps Harry could struggle at first with the basic tasks like feeding and changing the baby. He might make mistakes but learn quickly.
In fanfiction, if Harry Potter finds a baby phoenix, it could be a very magical encounter. The baby phoenix might be in need of protection. Harry, being the hero he is, would likely take it under his wing. He could use his knowledge of magical creatures from Hogwarts to care for it. Maybe the phoenix would grow up to be a powerful ally for Harry in his future adventures.
In many such fanfictions, there could be a lot of different scenarios. One possibility is that the wizarding world would be in chaos. Dumbledore might lead a frantic search for baby Harry. Maybe some of the Order of the Phoenix members would try to infiltrate Voldemort's lair to rescue him. It could also be that Voldemort has some strange plan for Harry, like trying to turn him to the dark side from a very young age.
Well, in such a fanfiction, baby Harry might experience a very warm and loving moment when he meets his parents. Maybe his parents would hold him gently, look at him with so much love in their eyes, and Harry would feel an instant connection to them.