One possibility is that Sesshomaru would become a sort of loner in Kagome's time. He's used to being a powerful figure in his own world, but here, he has to start from scratch. He might be intrigued by the concept of schools and learning, which is so different from what he knows. His interactions with Kagome could range from being hostile as he tries to assert his dominance, to gradually warming up to her as he realizes she's his key to adapting to this new time.
In fanfiction, if Sesshomaru were in Kagome's time, he might start to understand human society better. He could end up using modern things to his advantage. For example, he might use modern medicine to heal himself or his allies. And his relationship with Kagome could change. Instead of just seeing her as a nuisance in his own time, he could see her as a guide in this strange new world.
Well, he might be completely bewildered by all the modern technology. For example, seeing cars moving at high speeds on the roads could startle him. He could also have trouble adjusting to the social norms. Maybe he would accidentally draw too much attention to himself because of his unique appearance and old - fashioned ways of speaking.
If Kagome meets Sesshomaru in modern time in fanfiction, it could start with Kagome being in a busy city street and suddenly sensing a strange and powerful presence. She turns around and there is Sesshomaru, looking out of place in his traditional attire. At first, Sesshomaru might be tempted to attack Kagome, thinking she is some sort of nuisance in this new world he has found himself in. But Kagome, being the kind - hearted person she is, tries to defuse the situation. She might offer to help him find a way back to his own time or at least get used to the modern world. This could lead to a series of comical situations, like Sesshomaru trying to fit into a small elevator or being startled by the sound of a cell phone ringing. As time passes, they could form an unlikely friendship, with Kagome learning more about Sesshomaru's past and him starting to respect her more.
A possible plotline could be that Sesshomaru has to prove himself worthy to Kagome's family and friends. Since he has a reputation as a somewhat cold and aloof demon, this won't be easy. When Kagome gets pregnant, it adds more pressure. He has to show that he can be a reliable partner and father. Meanwhile, Kagome is trying to figure out how to combine her modern - world knowledge with the ways of the feudal era when it comes to raising a child.
Well, Kagome could end up helping younger Sesshomaru when he is injured. This would be a big shift in their relationship as Sesshomaru is not one to usually accept help from a human. But since he is younger, he might be more vulnerable and thus more likely to accept her aid.
Another scenario could be that Sesshomaru gradually realizes that kidnapping Kagome to mate was a wrong move. As he spends time with her, he sees her kindness and intelligence, and he starts to develop a different kind of respect for her, rather than just seeing her as a potential mate. So he might let her go in the end.
Well, she could try to find a way to return him to his normal form. Maybe she'll search for some ancient magic or consult with a powerful sorcerer in the feudal era.
Maybe it's part of a miscommunication plot. The author wants to show how misunderstandings can lead to harmful actions. Sesshomaru, being a complex character, could misinterpret Kagome's actions or intentions and end up hurting her accidentally. This would then lead to a journey of reconciliation and growth in the fanfiction.
Perhaps Sesshomaru sees some value in Kagome. Maybe he realizes that she has certain powers or knowledge that could be useful to him in the future, so he decides to save her from Inuyasha.
One possible storyline could be that through some magical or unforeseen circumstances, Kagome and Sesshomaru are brought together. Maybe they have to team up to face a common enemy. During this time, their relationship deepens and feelings develop. Eventually, Kagome becomes pregnant. The story could then focus on how they deal with this new situation, with Sesshomaru having to come to terms with his new role and Kagome adapting to the changes in her body and life.
One possible plot could be that Kagome discovers she's pregnant after an unexpected encounter with Sesshomaru. They then have to deal with the shock and the implications in a world where their relationship is not the norm. Sesshomaru might struggle with his new - found responsibilities while Kagome tries to adjust to the changes in her body and life.