Perhaps Harry time - travels and gets stuck in a time loop where his family keeps repeating the same day over and over. He has to figure out what is causing the loop and how to break it while also protecting his family from any threats that occur during that day. It would be a race against time and his own understanding of magic.
Another idea is that Harry travels to a time when his family was being hunted by Voldemort but in a parallel timeline. He could try to find a way to merge the timelines in a way that saves his family in both timelines. This would involve a lot of complex magic and decision - making on Harry's part.
Well, in a time travel fanfic, perhaps Harry accidentally travels back to the time when the founders of Hogwarts were still alive. He might learn ancient magic directly from them and use that knowledge to defeat Voldemort in his own time. Or Ron could go back in time and end up changing some Quidditch matches in the past, which then has unexpected consequences for the present, like different teams winning championships and changing the overall Quidditch culture at Hogwarts.
In a 'Harry Potter Dark Time Travel Fanfic', a character could travel back to the time of the first great wizarding war. They could attempt to save lives that were lost in that conflict, but in doing so, they unknowingly create new threats. For instance, saving a certain wizard might lead to that wizard being corrupted later and causing even more destruction.
One idea could be that Harry travels back in time to his parents' era. He uses his mastery of death to protect them from Voldemort. Maybe he can't directly interfere but finds a way to subtly change things, like giving his father a special charm that ends up saving their lives in a crucial moment.
One idea could be that the new generation discovers a time - turning device left by Hermione. They travel back to the time of the first Triwizard Tournament. There, they meet a young Sirius Black and Remus Lupin, and get involved in the mystery surrounding Cedric Diggory's death in a new way.
One idea could be that the next - generation characters travel back to the time of the first wizarding war. They could accidentally change some small events, which then have big consequences on their present time. For example, they might prevent a certain spell from being cast that was crucial in the defeat of a dark wizard, and now they have to figure out how to fix it in their own time.
Another plot idea could be a family that adopts a magical creature as a part of their family. In the wizarding world, this is quite unusual. The family then has to deal with the reactions of the wizarding community. They also have to learn how to take care of the creature, and the creature could end up helping the family in unexpected ways during their adventures in the Harry Potter - like world.
One idea could be exploring Harry's family vacations. Maybe they go to a magical beach where the kids learn special water - based magic. Another could be a story about Harry teaching his kids about the Marauder's Map and the adventures they have trying to find hidden passages in Hogwarts that even he didn't know about.
Well, perhaps Harry is adopted by a family of magical creatures, like centaurs. They teach him their unique ways of magic and understanding of the magical world. He could have a whole different perspective on things like divination, as centaurs are known for their prophetic abilities. It would be really interesting to see how he interacts with his human friends at Hogwarts after growing up in such a different environment.
Another plot could involve a member of the royal family in the Muggle world being a Squib. This person, desperate to be part of the magical world, tries to find a way to regain their magic through the help of the Potter family. The story could then revolve around the secrecy that needs to be maintained while also trying to help this person, and how it affects the relationship between the wizarding and Muggle royal families.
You could also focus on the Weasley - Potter family relations in a fanfic. For instance, how the two families' magic combined in different ways. Maybe there are some spells that only work when a Potter and a Weasley work together, and exploring those spells and the situations where they are used can make for a great fanfic story.