In a 'Harry Potter betrayed by Gryffindor' fanfiction, perhaps there is a prophecy that is misinterpreted. The Gryffindors think Harry is the cause of upcoming doom instead of the savior. So, they begin to betray him. Harry would then have to struggle not only with the external dark forces but also with the internal pain of being rejected by those he considered friends and housemates. He might start to question his own identity and values, and his journey would be about regaining the trust of Gryffindor or finding his own path without them.
Perhaps an old enemy who has infiltrated Gryffindor in disguise. They use their influence to make the Gryffindors believe that Harry is a danger. They could be a Death Eater or a follower of Voldemort who has found a way to get into Gryffindor and manipulate the students' minds, causing them to betray Harry.
One possible plot could be that Harry is framed for something he didn't do. Maybe a powerful dark object is found in his dorm, and the Gryffindor house, fearing for their reputation and safety, decides to exile him. Harry then has to prove his innocence while also dealing with the isolation and new challenges outside of his familiar house.
Well, perhaps in this fanfic, Harry could be wrongly accused of a serious crime like dark magic use. Everyone, including his friends Hermione and Ron, might turn their backs on him due to false evidence. He would then have to fight alone to clear his name and find out who really framed him.
Perhaps in the fanfiction, the Quidditch team gets influenced by a dark wizard who has a grudge against Harry. The wizard uses a spell to make the team members believe Harry is a threat to them. So they start to betray him by not passing the Quaffle to him during the game, or even colliding with him on purpose during a fly - around. This would lead to Harry feeling extremely isolated and confused as he thought his team was like family.
Perhaps he leaves Gryffindor in fanfiction because he is influenced by a new mentor or friend who is from a different house or group. This person might convince him that he can achieve more or be more true to himself outside of Gryffindor. Also, it could be due to a prophecy or a special mission that requires him to distance himself from Gryffindor for a while to protect the house or the entire Hogwarts from a certain threat.
Well, Harry Potter himself could be a possible heir. He already has so many Gryffindor - like qualities. His courage and loyalty make him a strong candidate.
One interesting plot could be that the descendant discovers a hidden chamber in Hogwarts that was sealed by Gryffindor himself. Inside, there are ancient spells and secrets that could change the wizarding world. The descendant has to battle dark forces who also want to get their hands on these secrets.
One possible plot could be that the godlike fem Harry Potter is betrayed by the wizarding establishment. They see her as a threat due to her immense power. So they conspire against her, which leads her to go into hiding. While in hiding, she discovers secrets about the wizarding world that were meant to be hidden and she uses this knowledge to fight back against those who betrayed her. She may also form new alliances with outcasts or creatures that were also wronged by the wizarding society.
Perhaps Harry Potter travels back in time and, for some reason, makes a deal with the dark side. He might be tricked into believing that by siding with Voldemort in the past, he can save more lives in the future. This betrayal could lead to a whole new chain of events, changing the relationships he has with his friends like Ron and Hermione.
Ron Weasley can also be thought of as an alpha in certain fanfictions. He has his own brand of loyalty and courage. When his friends are in trouble, he steps up. His growth throughout the series, from a sometimes - insecure boy to a confident young man, gives him alpha - like qualities in the context of Gryffindor.