The plot could start with Percy finding out about Annabeth's cheating. He would be devastated. Annabeth, on the other hand, might not have expected to feel so empty without Percy. So she decides she wants him back. At first, Percy doesn't want to hear anything from her. But Annabeth starts to befriend Percy's friends and family to get closer to him. Percy is conflicted because he still has feelings for her deep down. The fanfic could show how they both grow and change through this difficult situation, with Annabeth having to prove she's worthy of Percy's love again and Percy having to decide if he can move past the betrayal.
In such a fanfic, the plot could be very complex. Maybe Annabeth realizes she made a huge mistake. She might start by trying to approach Percy subtly, like showing up at his favorite places. But Percy would be hurt and angry. He might initially reject her attempts. However, as she keeps trying, she could start to show real remorse and explain the reasons for her cheating, which could be due to some external influence or her own insecurities. And Percy might gradually start to question his own feelings towards her again.
Well, if we consider this fanfic idea, perhaps Annabeth's attempts to get Percy back could involve her making grand gestures. For example, she could plan a big event where she publicly apologizes to Percy. But Percy has his pride and the trust has been broken. So he might not be so easily swayed. The fanfic could explore how Annabeth has to really dig deep into her character and change in order to even have a chance at getting Percy back. It would also show Percy's journey of dealing with the betrayal and whether he can ever truly forgive her.