One common theme is isolation. When Harry is betrayed, he often finds himself alone, cut off from his previous support systems. For example, in many fanfics, he has to leave Hogwarts or avoid his friends. Another theme is revenge. Sometimes Harry seeks revenge on those who betrayed him, which adds a darker element to the story.
He could be initially shocked. Harry, who has trusted Ginny deeply, would find it hard to believe at first. He might go through a period of denial, trying to find excuses for Ginny's actions.
In 'harry potter is betrayed fanfic', Luna Lovegood might be a character who betrays Harry. Maybe she is under the control of some mind - altering spell or has been deceived by a false prophecy that makes her think she is doing the right thing by betraying him. Also, Hagrid could be a shock betrayer if he is somehow forced to choose between Harry and his beloved magical creatures, and chooses the latter in a way that is seen as a betrayal to Harry.
In a 'Harry Potter betrayed fanfic', perhaps Hermione turns against Harry. It could be because she disagrees with Harry's more dangerous and reckless plans to fight Voldemort. She might think he's endangering too many lives without proper thought, and this leads to a rift and a sense of betrayal.
Even Ginny could be written as a betrayer in a fanfic. For example, if she becomes possessed by a dark force, she might turn against Harry. Her relationship with Harry is so central in the original story that a betrayal from her would be a huge shock and create a lot of drama in the fanfic.
One common plotline could be a friend turning against Harry due to jealousy. For example, Ron might be jealous of Harry's fame and betray him by revealing his secrets to the Death Eaters. Another could be a teacher who was thought to be trustworthy, like Snape in a different scenario, actually working against Harry all along. Or perhaps a new character introduced in the fanfic who befriends Harry only to betray him for some dark magic - related motives.
He might be extremely angry and confused. After all, parents are supposed to be the ones you can trust the most. He could start to question everything he knew about his family and himself.
In some fanfics, it might be for the sake of a more complex plot. The writer wants to create drama and conflict. So, Ginny could be made to betray Harry to add a new layer of struggle to Harry's life. It could also be related to her family loyalty. If the Weasley family was somehow forced into a difficult situation where they had to choose between Harry and their own safety, Ginny might be written to make a choice that seems like a betrayal to Harry.
A great 'betrayed Harry Potter fanfic' is 'Alone and Betrayed'. This story takes a different turn where Harry is not only betrayed by friends but also by some of the Hogwarts faculty. He has to rely on his own wits and some unexpected allies to fight against the forces that are trying to bring him down.
Another possible betrayer could be Dumbledore in some darker fanfictions. He might have a hidden agenda all along. He could be using Harry as a pawn in a much larger and more sinister game. And when Harry starts to figure things out and goes against Dumbledore's plans, Dumbledore betrays him to keep his own plans on track.