A possible plot is that the daughter has to deal with the legacy of her parents. Since Hermione was a Muggle - born and Sirius was a Black, she has to face the prejudices that still exist in the wizarding world. She might decide to fight against these prejudices, following in her parents' footsteps. She could start a movement at Hogwarts to promote equality and acceptance, and along the way, she has adventures and makes new friends who support her cause.
Perhaps the daughter discovers she has a unique magical ability that neither Hermione nor Sirius had. This could lead her on a journey to understand this power and its origin. She may also find herself in the middle of a conflict between different wizarding factions who either want to use her for her abilities or are afraid of what she can do. In the fanfiction, she could also have a group of loyal friends who help her through these challenges.
One idea could be that the daughter inherits Hermione's intelligence and Sirius's rebellious spirit. She might use her smarts to uncover secrets about the wizarding world that were long buried, like hidden spells or lost histories. Another plot could involve her struggling to fit in at Hogwarts, being the daughter of two such well - known figures. She could face both envy and admiration from her peers.
Another plot could be set in an alternate universe where Sirius never went to Azkaban. He and Hermione meet when she is a young, brilliant witch just starting at Hogwarts. Sirius, being a bit of a rebel, takes Hermione under his wing and they embark on adventures outside of the school rules, exploring the Forbidden Forest together and uncovering secrets about the wizarding world that are not taught in classes.
A possible plot is a mystery - solving one. There's a strange magical occurrence in Hogwarts that is affecting both Gryffindors and Slytherins. Hermione starts investigating, and she enlists the help of Sirius (who could be a ghost or somehow back in a semi - corporeal form). Harry is naturally drawn to help Hermione, and Draco gets involved because it might affect his family's standing. As they dig deeper, they find out that it's an ancient curse set by a long - forgotten wizard, and they have to find a way to break it using their combined skills and knowledge.
One interesting plot idea could be that during the game, Sirius is dared to reveal a long - held secret about his family. For example, a hidden family heirloom or a mysterious relative. Another idea is that Hermione is asked to tell a truth about her feelings towards one of her Hogwarts professors, which leads to some awkward yet comical moments. A third plot idea might be that they are dared to switch magical abilities for a day, leading to chaos as Hermione tries to handle Sirius' more impulsive and powerful magic and Sirius struggles with Hermione's more studious and precise spells.
A great plot idea would be that when they time travel, they accidentally change something in the past that has a huge ripple effect on the future. They then have to figure out a way to fix it. Maybe they make it so that Sirius was never disowned by his family in the past, which changes his whole life trajectory. This could lead to a completely different future for the wizarding world, and they have to race against time (again) to make sure the future doesn't go completely haywire.
Well, perhaps there's a fanfiction where Sirius Black is wrongly accused again, but this time Hermione believes in his innocence from the start. She uses her intelligence and resources to prove his innocence while they are on the run from the Ministry. Along the way, they form a deep bond and discover new magical abilities within themselves that they use to clear Sirius' name and also make some changes to the wizarding world's justice system.
A plot could involve the daughter using her unique position to bring about peace. Since she has a connection to both the 'good' side through Hermione and the 'dark' side via Bellatrix, she could be the key to bridging the gap between the two warring factions. For example, she might use her knowledge of both sides' secrets to negotiate a truce.
One idea could be the daughter's struggle to break free from the dark reputation of the Lestrange name while also dealing with her mother Hermione's fame as a hero. She might face discrimination in the wizarding world due to her family name, but strive to prove herself through her own magical abilities and kind heart.
Another plot could involve the daughter discovering a long - hidden secret about her parents' relationship. Maybe there was a prophecy that led to their union, and she has to figure out how to deal with the implications of this discovery. She could be hunted by dark forces who want to use her for their own gain because of her unique heritage.
One possible plot idea could be that Sirius catches Harry and Hermione in the middle of a secret plan to save a fellow student from a dark magic threat. Sirius, initially thinking they're up to something dangerous, then realizes their noble intentions and decides to help them. Another idea is that Sirius catches them while they are exploring a hidden part of Hogwarts that is related to an old mystery about his family. He then shares his knowledge about it with them, leading to an exciting adventure.
One idea could be that Severus discovers Hermione is in danger from some dark magic users due to her intelligence and Muggle - born status. He takes it upon himself to protect her like a father would. For example, he could secretly follow her around Hogwarts, using his skills in potions and the Dark Arts to thwart any threats.