In a fanfiction where Harry is raised by Narcissa, it could start with Narcissa finding baby Harry after the death of his parents. She decides to raise him as her own, away from Dumbledore's influence. As he grows up, Harry discovers his true heritage through Narcissa's careful revelations. He may be taught magic in a way that combines the Blacks' traditional magic with some new elements. His relationship with the other Hogwarts houses would be very different. He could be more of an enigma to Gryffindor, but have a closer connection to Slytherin. His story arc would involve him trying to find his place in a world that is both fascinated and suspicious of his upbringing.
Well, a plot could involve Harry being raised by Narcissa Black in a world where the wizarding world is more divided than ever. Harry, influenced by Narcissa, has a different view on blood purity. He could be trained in dark arts defenses in a more Slytherin - like way. This would make his battles against Voldemort very different. He might also have a closer relationship with Draco from the start, and they could end up as allies rather than rivals. Plus, Narcissa's influence could lead Harry to have a more nuanced understanding of the Death Eaters, which would add a lot of complexity to the story.
Another plot could be a time - travel fanfiction. James Potter somehow travels to a time when Narcissa is young and in a difficult situation. He decides to help her, and in the process, they form an unexpected bond. This bond then has consequences for the future as James returns to his own time.
One idea could be a story where Bellatrix and Narcissa are forced to work with Harry Potter due to some dark magic that binds them, and a lemon tree (represented by 'lemon' in a symbolic way perhaps) holds the key to breaking the spell. Another could be a tale set in an alternate universe where they all have to protect a magical lemon that has the power to save the wizarding world.
One interesting plot idea could be that Snape, in raising Harry, teaches him advanced potions from a very young age. Harry becomes a prodigy in potions, much to the surprise of the other Hogwarts students. Another idea is that Snape's strict but fair upbringing makes Harry more reserved and less impulsive, which changes the way he interacts with his friends. He might be more cautious and calculating in his actions, especially when dealing with enemies like Voldemort.
One plot idea could be that Harry discovers a hidden magic within the orphanage itself. Maybe there's a secret room that holds ancient spells or a connection to a long - forgotten wizarding family. Another idea is that the other orphans start to show signs of magic too, and Harry has to figure out how to protect them from the wrong kind of attention. Or perhaps the orphanage is under a curse, and Harry's presence there is the key to breaking it.
One plot idea could be that Harry's grandparents are very strict about magic, so he has to secretly practice. Another could be that they are part of a secret wizarding society that has been in hiding, and Harry discovers their secrets. Or perhaps they have a special connection to Voldemort's past that Harry uncovers.
One plot idea could be that Shield trains Harry in combat and espionage skills from a young age. This makes him a more physically and tactically adept wizard compared to the original story. He might use his new skills to uncover dark secrets within the wizarding world earlier.
One idea could be that Harry discovers Narcissa has a secret mission to undermine Voldemort from within. Maybe she's been secretly helping the Order of the Phoenix all along and Harry stumbles upon this knowledge.
In the fanfiction, it could be interesting if Harry uses his magic to protect the other orphans from bullies. He might not fully understand his powers yet, but his instincts kick in. And then when he finally gets his Hogwarts letter, the other orphans are both sad to see him go but also excited for him, and he has to figure out how to leave the only home he's known while also being eager to enter the wizarding world.
One idea could be that Harry grows up with cat - like reflexes and stealth. He might be able to move around Hogwarts unnoticed more easily, like a cat prowling in the shadows.
One interesting plot could be how Harry's magical abilities are perceived in a world of nations. Maybe he uses his magic to solve international disputes. Another idea is that different nations try to influence his upbringing, each adding their own cultural and magical elements to his training.