Argus Filch might seem like an unlikely choice, but think about it. He's always been bitter about his position in Hogwarts. In a fanfiction, he could be the mob boss of a group that steals and sells Hogwarts' lost items. He knows all the nooks and crannies of the school, which would give him an advantage in running his illegal operation.
Bellatrix Lestrange, if she had survived the Battle of Hogwarts. She was extremely powerful and deranged. She could rule the wizarding underworld with an iron fist, using fear and torture to keep her subordinates in line. Her loyalty to Voldemort could be transferred to her own self - serving criminal empire.
Voldemort could be a very likely mob boss character. He already has an army of Death Eaters and is used to ruling with an iron fist. His thirst for power and lack of regard for the rules of the wizarding world would make him a very menacing mob boss in this type of fanfic.
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.
An unknown wizard from a far - off land could be a thief in Harry Potter fanfiction. This wizard could come to Hogwarts or the wizarding world of Britain with the intention of stealing unique magical items that are not found in their own land. They would bring a sense of mystery and a new cultural perspective to the story.
One potential character could be a new student who arrives at Hogwarts with a mysterious past. He shows extraordinary magical abilities that seem a bit too dark for the normal wizarding world. Another could be a distant relative of Draco Malfoy. Since the Malfoys have a history with the dark arts, it wouldn't be too far - fetched for one of them to be revealed as the heir of Sauron. Or perhaps an old wizard who has been in hiding for centuries and resurfaces as the heir of Sauron.
Fred Weasley could also be seen as a ladies' man. He's funny, outgoing, and always up for a good time. Fanfiction could explore how his humorous and mischievous nature draws the girls to him. He might be the type to play pranks on the girls just to get their attention and then charm them with his witty remarks.
In this fanfiction, the plot might revolve around Harry's transformation into a mob boss during time travel. He could discover that the wizarding world has a seedy underbelly that was hidden from him before. Harry may start to use his magic in new and unethical ways to gain power. He might face challenges from other powerful wizards who don't want a new player in the mob scene. His friends, like Hermione and Ron, could be conflicted about whether to support him or try to stop his descent into the dark side of the wizarding world.
Another possibility is that the heiress could be a new character entirely, created by the fanfiction author. She could be from a foreign wizarding family that has a claim to something in the British wizarding world. This new character could bring in different cultural elements of magic and challenge the traditional ways of the Hogwarts - centered wizarding society.
One possible plotline could be Harry taking over the wizarding underworld after defeating Voldemort. He might use his fame and the loyalty of his friends to start building his own 'empire'. He could control the trade of magical items and potions, similar to how a mob boss controls illegal trades. Another plotline could be Harry being born into a mob - like wizarding family instead of the Dursleys, and growing up learning the ways of the wizarding underworld from a young age.
Another possibility is a reformed dark wizard. Someone who has seen the error of their ways and now uses their in - depth knowledge of dark magic to teach students how to defend against it. This character would have a very interesting backstory, having once been on the wrong side but now using their experiences to help the next generation of wizards in the DADA class.
A long - lost relative of Sirius Black could be a shapeshifter. Since the Blacks had many secrets and were involved in a lot of dark magic in their family history, it would be believable for a hidden relative to have this unique ability.