There could be. The Harry Potter fandom is huge and very creative. Writers like to explore different concepts and personas for the well - known characters. A 'Harry Potter is a mafia king' fanfiction would be a very different take on the character, but it's entirely possible that it exists out there among the countless fan - made stories.
The 'Harry Potter Heir of Mafia' fanfiction might center around a plot where the main character, who has ties to the mafia in some way, navigates through the wizarding world. It could be that they use their mafia - influenced skills or knowledge, such as strategic thinking or a sense of loyalty and family (but in a mafia context), to deal with the challenges in Hogwarts or the broader wizarding community. For example, they might face off against dark wizards in a way that's different from the traditional Hogwarts students because of their mafia - like upbringing.
One could imagine that a distant relative of the Black family, who has been disgraced or cast out, becomes a mafia boss. They still have some of the Black family's wealth and dark magic knowledge, but use it in a more criminal way. For example, they could be running a protection racket in Knockturn Alley, threatening shop owners to pay up or face dark magic. Severus Snape also could potentially be a mafia boss in an alternate story. He has the intelligence and the ability to be secretive. He could be using his potions expertise to create and sell illegal or dangerous potions on the black market, while also maintaining a network of spies and henchmen within Hogwarts and the wizarding world.
Well, the plot could start with Harry being found by the mafia after some sort of accident or escape from the Dursleys. The mafia, seeing his potential and his lack of a proper family, decides to take him in. They would train him in their ways, which could include things like combat and stealth. Harry might then have to navigate between the mafia's underworld and the wizarding world, trying to keep his two lives separate while also using his new skills to fight against the Dark Lord.
In a 'Harry Potter Raised by Mafia' fanfiction, Harry's moral compass would be greatly affected. He may not have the same sense of right and wrong as in the canonical story. The mafia family could use his fame as 'The Boy Who Lived' for their own gain, perhaps in the wizarding underworld. He might also be involved in illegal magical activities from a young age.
Power struggles are a common theme. Just like in real mafia stories, in 'Harry Potter mafia family fanfiction', families or groups fight for control over certain areas of the wizarding world, be it magical resources or influence. Another theme is secrecy. These mafia - like families often have many secrets that they are desperate to keep hidden from the rest of the wizarding community.
The character transformations are often very interesting in these fanfictions. Characters from the original Harry Potter series may take on new roles and personalities in the mafia - influenced world. They might have to make tough choices between their magical ethics and the mafia code, like in 'The Dark Lord's Heir' where Harry has to decide how far he'll go to protect his newfound mafia family while still holding onto his values as a wizard. Also, the power dynamics are different. Instead of just the good vs. evil of the original series, there are complex hierarchies within the mafia organizations in the fanfictions.
Fanfiction.net is also a good place to look. It has been around for a long time and has a large number of Harry Potter fanfictions. Just be sure to use the search function and look for tags related to 'mafia' to narrow down your search to the ones you're interested in.
One interesting 'Harry Potter mafia fanfiction' could be the ones where the wizarding world's dark underbelly is explored through the mafia concept. For example, some stories might depict the Death Eaters as a sort of mafia organization, with Voldemort as the feared don. They could be involved in illegal magical activities like the black market trade of dark artifacts and controlling certain parts of the wizarding underworld.
One possible plotline could be Harry rising to power within the wizarding mafia world. He might start from a small - time operator and gradually build his empire. Another could be his conflicts with other powerful wizarding families who are also involved in mafia - like activities. He would have to use his magic and wits to outmaneuver them.