The puppy could be a gift from one of Harry's friends. It might have special powers that help Harry in his adventures. For example, it could sniff out dark magic or lead Harry to hidden passages. And Harry would have to take care of it, which would add a new dimension to his already busy life at Hogwarts, having to juggle classes, Quidditch, and fighting Voldemort.
Maybe the puppy is a stray that Harry finds near the Forbidden Forest. He takes it in and names it something like 'Shadow'. The puppy becomes very loyal to Harry and helps him in unexpected ways. It could be that when Harry is in danger, the puppy's barking alerts his friends or it even has the ability to transform into a more powerful magical being for a short time to protect Harry.
It could mean that there is a fan - made fictional work where Harry Potter is somehow related to a puppy. Maybe in this fanfic, Harry Potter has a pet puppy or there are some adventures involving puppies in the Harry Potter - like world.
I'm not sure if it's a popular type. It depends on how many fans are interested in combining Harry Potter with puppies. Some people might find it a really unique and cute idea, but others might be more into the traditional aspects of the Harry Potter world without adding puppies.
Well, there could be a 'Harry Potter Puppy Fanfic' where the puppy is actually a transformed wizard. Maybe they were cursed and turned into a puppy. This puppy then tries to find a way to break the curse while interacting with the main characters. It could add a really cute and unique element to the Harry Potter universe. There might also be a story where a puppy is found by Hermione and she decides to take care of it while also teaching it some basic magic tricks.
I'm not entirely sure specifically as 'puppy play' in fanfic can be a rather strange and perhaps not very common concept in the context of Harry Potter. It might be some sort of role - playing or AU (alternate universe) idea where characters take on puppy - like behaviors or characteristics in a fan - created story, but this is just speculation.
I'm not aware of any particularly popular 'harry potter puppy play fanfic' stories. This is a rather unusual concept and not something that is likely to be mainstream within the large and diverse Harry Potter fanfic community.
One way could be through a magic spell gone wrong. Maybe Harry was trying to transform into an Animagus but something went awry and he ended up with the mind of a puppy instead of the intended animal. He'd then have to figure out how to reverse it while dealing with his new puppy - like instincts, like chasing his own tail or getting distracted by squirrels.
A fanfic with 'Harry Potter has a bug demon mate' could start with Harry discovering this strange being. The bug demon mate might look quite unusual, with features that are part bug and part something else. At first, Harry might be a bit wary, but as they interact more, they realize they can work together. The bug demon could have the ability to communicate with other bugs, which could be used for gathering information. For instance, it could send out bugs to spy on the Death Eaters. Their friendship could be a key element in the fanfic, and the bug demon's loyalty to Harry could be unwavering as they face various challenges together in the wizarding world.
Well, perhaps the tattoos could be a mark of a secret society within the wizarding world that Harry gets involved in. They might give him special powers or knowledge.
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.
You can try fanfiction websites like Archive of Our Own (AO3). It has a large collection of fanfics including 'Harry Potter Puppy Fanfic'. Just search for the relevant keywords and you'll likely find some interesting stories.