Harry Potter is the main character as the title implies. His friends from Hogwarts such as Hermione, Ron, and Neville could be main characters too. However, the fanfiction might introduce new characters related to Tartarus. For example, there could be a character who is a messenger from Tartarus or a guardian of the secrets related to Harry's father. These new characters could add more complexity and mystery to the story, and they would interact with Harry and his friends in various ways, either helping or hindering them in their journey.
Obviously, Harry Potter would be one of the main characters. Since it's about him being the son of Tartarus. And probably his friends like Hermione and Ron would also be important characters as they are in the original series. They might react differently to Harry's new identity.
In the 'Harry Potter Son of Tartarus' fanfiction, Harry Potter is the central figure. But there could be other characters as well. Dumbledore might play a crucial role as he usually does in guiding Harry. And if the story delves into the nature of Tartarus, there could be new characters introduced who are related to Tartarus in some way, like maybe some ancient beings or wizards who know the secrets of Tartarus and have a connection to Harry.