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.
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.
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.
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.
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.
The puppy would add a lot of fun. Harry would have a new friend to play with. He could take the puppy for walks around the Hogwarts grounds. It would also give him a sense of responsibility outside of his usual wizarding duties.
In a fanfiction, Sirius as a puppy Animagus might have a special bond with Harry's Patronus, which is also a stag. Since he was Harry's godfather, this connection could be explored in a really interesting way. For example, the puppy Sirius could be drawn to the Patronus and they could communicate on a deeper level, perhaps sharing memories or emotions that are unique to them. It could add a whole new layer to the magic in the Harry Potter universe.
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.
Well, just based on that title alone, it's difficult to determine its quality. There are so many aspects that make a Harry Potter fanfic great. For example, it could explore new relationships between the characters, or create exciting new magical adventures. But we don't know if 'skull is harry potter fanfic' does any of those things. So, it might be good, it might not.