One plotline could be that they are both trying to uncover a family secret. Maybe there's something about their parents or ancestors that has been hidden, and they have to work together to find out the truth. Along the way, they face various obstacles and make new friends who help them in their journey.
Well, they could start off with some initial misunderstandings. Maybe Hermione, being as intelligent as she is, could initially be suspicious of Jasper's motives. But as the story progresses, they could discover they have common interests, like a love for ancient magic or a desire to protect their world from a new threat.
There's no one definitive version of Jasper's sister in fanfiction. Different authors will create different characters for her. Some may make her a powerful vampire who has been around for a long time and has a lot of knowledge. Others may portray her as a newly - turned vampire still adjusting to her new existence and learning from Jasper about the ways of the vampire world.
I haven't come across a fanfiction where Hermione is Major Jasper's mate in a lemon context. However, fanfiction writers are very creative and it's possible that someone out there has written such a story. You might have to search through various fanfiction platforms like Archive of Our Own or FanFiction.net to find out.
The'major' could be Hermione's area of study. Maybe it's something unique in the fanfiction world that combines elements of magic related to Jasper. For example, if Jasper has some special power, the major could be about understanding and harnessing that power.
One idea could be a crossover where Jasper Hale, with his vampire abilities, senses Hermione's powerful magic. They meet when the Cullens move to the UK for some reason. Jasper is intrigued by Hermione's intelligence and her ability to handle complex situations. They start to form an unlikely friendship which gradually turns into a deeper relationship as they learn more about each other's worlds.
In some Twilight fanfictions about Jasper's sister, she might be portrayed as having unique powers. For example, she could have enhanced mental abilities like being able to sense the emotions of vampires from a greater distance than Jasper. She may also play a role in the complex vampire society, perhaps being involved in the power struggles between different vampire covens.
Well, one possible plot could be that Hermione, being Jasper's niece, discovers some hidden magical abilities in the family. Maybe she stumbles upon an old family spellbook that only the family's descendants can access. This could lead her on an adventure to learn more about her family's magical past and how it relates to the wizarding world at large.
You can start by looking on fanfiction.net. It has a vast collection of fanfictions from various fandoms, and there's a good chance you'll find jasper and hermione fanfiction there.
There's also 'Jasper and Hermione: The Unexpected Alliance'. In this fanfiction, they could be brought together by a common threat that neither of their normal allies can handle. It delves into their characters as they learn to trust and rely on each other in this new situation.