Maybe the baby dragon is a rare species. This would attract the attention of magical zoologists and collectors. Harry would then have to deal with the ethical issues of keeping the dragon or giving it to those who claim to study it properly. He would also need to consider the dragon's own well - being and freedom.
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.
One interesting fanfiction could be about baby Harry's first magical experiences even before he went to Hogwarts. Maybe he unknowingly made his toys levitate when he was really young, and his aunt Petunia was terrified but couldn't figure out what was really going on.
Well, in these fanfictions, the theme of unexpected relationships is quite common. Snape and Harry having a father - son like relationship is something that was not in the original series. Also, the theme of hope is there. Despite all the difficulties and the dark world they live in, the presence of baby Harry gives Snape hope for a better future. And then there is the theme of self - discovery. Snape discovers new aspects of himself as he takes on the role of a caregiver for Harry.
Obviously, Harry Potter himself is a central character. His wife, whether it's Ginny or in some alternate scenarios someone else, would also be very important. Then there are his friends like Ron and Hermione. They would likely be the baby's godparents or play important roles in the baby's life. Dumbledore, even though he's passed away, might still have an influence through his wisdom left behind. And of course, there could be new characters created specifically for the fanfic, such as a nanny or a tutor for the baby with some unique magical skills.
One popular 'Harry Potter has baby' fanfiction could be 'The Next Generation' which explores the adventures of Harry's children at Hogwarts. It often focuses on their unique abilities and how they navigate the challenges of being the children of such famous wizards.
These fanfictions are also popular because they can explore different family dynamics. Harry grew up without his parents, so seeing him as a father creates an interesting contrast. It gives writers a chance to show how Harry might raise his child differently, based on his own experiences. Moreover, it can introduce new magical concepts related to the baby's abilities or the family's heritage, which is always exciting for fans.
The baby could be the child of a minor character from the original series who was in hiding. For example, the baby might be the offspring of a wizard who was on the run from Voldemort's followers and unfortunately didn't make it, leaving the baby behind for Harry to find.
Well, they could have all sorts of adventures. Maybe the baby cousin has some sort of special magic that Harry doesn't know about yet. For example, the baby cousin could be able to communicate with magical creatures in a unique way. And Harry, being the curious and brave wizard he is, would want to explore this new aspect of magic with his little cousin. They might go on a journey to find a rare magical creature that only the baby cousin can sense.
The fanfic could also be about how Harry's past experiences shape his parenting. Given his own difficult childhood, he would be extremely determined to give his baby a loving and secure environment. He might teach the baby about the importance of friendship and courage from a very young age, and the baby could grow up with a strong sense of justice, much like Harry did.