Beth Thomas in the story is a girl who had experienced early childhood abuse. She was then adopted and became known for her very difficult and disturbing behaviors such as harming animals and being overly aggressive towards people.
Alexis might confront Beckett directly. She could say something like 'I think you're cheating on me. What's going on?' This is a very straightforward approach.
I don't know who Alexis is in this story without reading it. But it's likely that Alexis is either the main character or an important figure in the events that unfold in the 'creepy subway' setting.
A lawyer could be an important character. This lawyer takes on Alexis's case, believing in their innocence. The lawyer has to battle a corrupt legal system or powerful opponents who want to see Alexis locked up for good. The fanfic could show the lawyer's strategies and how they build a case in Alexis's favor.
Since we don't have much information, Beth Anderson could be the author or the main character of this 'never - ending story'. Maybe she's a creative individual who has a lot to share through this story.
Perhaps there have been some rumors or whispers in their fictional world that have reached Alexis' ears. Even if they are baseless, they can plant the seed of doubt in Alexis' mind, making her think that Kate is cheating.
She could be defensive of Beckett. Since Alexis probably has a good relationship with Beckett, she may try to convince Castle that he's wrong and that Beckett didn't mean any harm. For example, she might tell Castle about all the positive things Beckett has done for her.
Yes, Beth Harmon is a fictional character from the novel 'The Queen's Gambit' by Walter Tevis, not a real - life person. However, the story was inspired by the world of chess and the experiences of real chess players to some extent.