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.
Harry can start by being completely honest with Draco. He should sit down with Draco and tell him about all his recent activities, who he has been with, and why. For example, if he has been working on a project with a classmate, he can explain the details of the project.
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.'
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 some fanfictions, Harry could rely on the help of his friends. Hermione, with her vast knowledge of magic and Hogwarts' rules, might find some overlooked evidence. Ron, with his loyalty and sometimes unexpected insights, could also play a part. Together, they could present a solid case for Harry's innocence.
In the context of a fanfic, Magnus might use his magic in a positive way. He could create a magical bond or a truth - revealing spell between him and Alec (with Alec's consent, of course). This would allow Alec to see into Magnus' thoughts and feelings, and he would know for sure that Magnus is not cheating. Magnus could also start spending more time with Alec and less time on his own or with other people, at least until Alec's suspicions are completely gone.
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.
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?'
If Harry has any special magical abilities or items that were overlooked, he could use them. For instance, if he still has the Marauder's Map, he might be able to find hidden passages in Azkaban to communicate with the outside or find evidence within the prison that clears his name. Also, his relationship with magical creatures like the Thestrals might come in handy. If they can be made to testify or help in some way, it could be a way to prove his innocence.
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.
I really hope there isn't such a fanfiction. Ginny and Harry have a strong and loving relationship in the original story, and creating a fanfiction with such a negative and unfaithful plot goes against the essence of their relationship.