She might confront Harry directly. In the heat of the moment, she could burst out with her suspicions and demand an explanation. For example, she might say, 'Harry, I've noticed you've been acting strange around that girl. Are you cheating on me?'
Ginny could also become very cold and distant towards Harry. She might start to avoid him, not answering his calls or messages in the fanfic. She would be too hurt and angry to be around him, thinking that he has betrayed her trust.
She is probably angry and frustrated. She would demand Castle to explain why he thinks so and would be hurt that he doesn't trust her.
Alternatively, Ginny could be very mature about it. She might respect Harry's decision, even though it hurts. She could choose to step back and give Harry the space he seems to need while secretly hoping that he will change his mind in the future.
Maybe she saw Harry spending a lot of time with another girl without proper explanation. In a fanfic, it could be that Harry is often with a new female character in his study or on some secret missions, and Ginny misinterprets this as something more than friendship.
Harry could also go into a state of shock and disbelief. He loves Ginny deeply, and to find out she's cheating would shatter his world. He might start to question everything about their relationship, like all the memories they've shared together. And he could become very withdrawn, not wanting to talk to anyone, even his closest friends like Ron and Hermione. He would need time to process his emotions and figure out what to do next.
She might directly ask him about her suspicions. Just come out and say 'Harry, I think you're cheating on me. I've noticed you acting strange lately.'
Kate might get defensive right away. She could say things like 'How could you think that of me?' and be angry at Alexis for not trusting her. This is a common reaction when someone is wrongly accused in a fanfic or in real life.
He could start by being completely honest with Ginny. Sit her down and tell her everything he has been doing, leaving no details out. For example, if he was working on a project with another character, he should explain the nature of the project, who else was involved, and why he had to keep it somewhat of a secret.
Ginny might be heartbroken at first. She could retreat into herself, spending a lot of time alone in her dormitory or in secluded places around Hogwarts. She may cry a lot and avoid socializing with their mutual friends.
Well, it could be that Harry has started acting really distant from Ginny. He might be canceling their dates frequently or not being as affectionate as he used to be. In the fanfiction, Ginny might also find some strange gifts or notes that she suspects are from another girl to Harry, which makes her think he's cheating.
In the fanfiction world, miscommunication often plays a big role. Perhaps Harry was involved in some secret mission or task that he couldn't tell Ginny about right away. But Ginny, not knowing the real situation, might misinterpret his secrecy as cheating. For instance, he might be sneaking around to protect Ginny from a potential threat, but she doesn't see it that way.