Well, a possible plot is that Harry discovers his true parentage in a very dramatic way. He could be in the middle of a battle or a difficult situation at Hogwarts and suddenly realize that Snape and Bellatrix are his parents. This would completely change his perception of himself and his place in the wizarding world. He might then have to deal with the consequences of this revelation, such as how the Order of the Phoenix and the Death Eaters view him.
In some fanfictions, the plot could revolve around Harry's magical abilities being a unique blend due to his parentage. He might have an uncanny ability with both light and dark magic. For example, he could be able to use some of Bellatrix's powerful dark spells in a way that is not completely evil, perhaps to defend against greater threats. His relationship with Dumbledore could also be very different. Dumbledore might be more cautious or more intrigued by Harry, depending on how he views the combination of Snape and Bellatrix's genes in Harry.
In some fanfictions, there might be a plot where Bellatrix and Harry are forced to team up against a greater evil. For example, a new dark wizard emerges who is more powerful than Voldemort, and they have to put aside their differences. Bellatrix, with her knowledge of the dark arts, and Harry, with his courage and Gryffindor spirit, make an unlikely but effective duo.
Yes, there are some fanfictions with such a wild and unorthodox concept. However, this goes completely against the original 'Harry Potter' canon which clearly states Harry's parents are James Potter and Lily Evans. In fanfiction, writers often like to explore 'what - if' scenarios that are far from the original story line, just for the sake of creativity and exploring different character dynamics.
Harry in this fanfiction might be a lot more complex. His identity is no longer that of the Boy Who Lived in the traditional sense. He has to come to terms with the fact that his parents are two very different and controversial figures. He may become more of an outcast, even among his friends at Hogwarts. His sense of right and wrong could be more blurred, as he has the influence of Bellatrix's dark ways and Snape's own morally ambiguous actions. He might be constantly questioning his own nature and whether he is destined to follow a path of good or evil.
One possible interesting plot could be Snape having to follow Harry Potter's lead in a dangerous mission. Maybe they are in a situation where Snape has no choice but to trust Harry completely, which is a big change from their usual relationship in the original books.
Perhaps in the fanfiction, Snape assigns Harry to clean all the old potion vials in the storage room during detention. While doing so, Harry discovers an old diary that seems to hold secrets about Snape's past at Hogwarts, which then leads to a series of revelations and a change in their relationship.
One interesting plot could be Harry growing up with Snape's strict but ultimately caring guidance. Snape might teach Harry potions from a very young age, and Harry could develop a different kind of magic skill set compared to canon. Another plot could involve Harry having to deal with the Slytherin side of the wizarding world earlier, as Snape has strong Slytherin ties. Also, the relationship between Harry and Snape could be a complex mix of father - son dynamic and teacher - student relationship, which would be really fascinating to explore.
Perhaps a plotline where Harry discovers the truth about his parentage later in life. He has been raised believing Bellatrix is his mother, but then uncovers evidence that it's all a complex web of dark magic and deception. This could lead to a journey of self - discovery as he tries to figure out who he really is and where he belongs in the wizarding world, all while dealing with the stigma of being associated with Bellatrix Lestrange.
One interesting plot could be Snape raising Harry while secretly training him in advanced potions and dark arts defenses. Harry would grow up with a different perspective on Snape, seeing him as a strict but caring father figure. Another plot might involve Snape having to protect Harry from other dark wizards who suspect Harry's true potential. This could lead to some intense magical battles and Snape using his knowledge and skills to keep Harry safe.
A really unique plot could be Snape adopting Harry during a time when Voldemort is still a threat. Snape has to balance protecting Harry from Voldemort's followers and also from the prejudice within the wizarding community. He might train Harry in Occlumency more intensively, and in the process, they develop a deeper understanding of each other. Harry starts to see Snape not as the mean professor but as a complex person with his own traumas and reasons for his actions.
Perhaps in the fanfiction, Harry is magically bound to please Snape in academic tasks. So, he has to study extra hard in Potions class and other subjects Snape is involved in. This might result in a transformation of their relationship, from animosity to a grudging respect as Snape starts to see Harry's efforts.