In some fanfiction, Jon Arryn's son could be a key figure in an alternative plot. For example, he might have been trained by a powerful wizard or warrior in the far north. This training gives him unique skills and knowledge. He then uses these to influence the power struggle in Westeros, perhaps by allying with certain houses against the Lannisters or even the White Walkers.
One interesting fanfiction could be about Jon Arryn's son surviving in secret and emerging to claim his father's legacy. He might have been hidden away by a loyal servant and grows up in exile, learning the ways of the world far from the politics of King's Landing. When he returns, he causes a stir as he tries to uncover the truth about his father's death.
A fanfiction could also explore a scenario where Jon Arryn's son has a special bond with a dragon. Maybe he discovers an ancient egg and through some magical event, hatches it. With his dragon, he becomes a force to be reckoned with. He could then use this newfound power to reshape the political and military landscape of Westeros, trying to bring justice and peace in the name of his father.
Perhaps the OC son has a special ability or gift that Jon Arryn was trying to protect him from being exploited for. After Jon Arryn's death, the son has to learn to control this ability while also dealing with the power struggles in King's Landing. He could be a key figure in the fight against the White Walkers, using his unique skills to help the living, all while trying to uphold his father's legacy.
The OC son could start off as a naive and sheltered young man, but after Jon Arryn's death, he is forced to grow up quickly. He becomes more cynical and distrustful of those around him, especially the nobles in King's Landing.
One idea could be that this adult son might have been involved in the political intrigue in King's Landing. He could have been a rival to Littlefinger, using his father's influence and his own wits to try and maintain the stability of the realm. Maybe he would have uncovered some of Littlefinger's schemes earlier, preventing some of the chaos that ensued in the series.
Suppose Jon Arryn's son forms an alliance with the Iron Islands in fanfiction. This would be a very different scenario from the original plot. With the Iron Islands' naval power and his own claim to power in the mainland, they could create a new power bloc. This could disrupt the balance of power between the other houses and change the way wars are fought and alliances are made in Westeros.
He could impact the story by influencing the Vale. Since Jon Arryn was an important figure in the Vale, his son would have had a certain amount of power and respect there. He might have been able to raise an army from the Vale earlier than what happened in the original story, and this army could have been a deciding factor in battles, like the ones during the War of the Five Kings.
There isn't a great deal of information about Arryn Blackfyre in the 'Game of Thrones' universe that is widely known. However, if we consider the context of the Blackfyre family in general, they were always a threat to the ruling Targaryens. Arryn Blackfyre might have been involved in the various political machinations and military campaigns that the Blackfyre family launched over the years. He could have been a key figure in their attempts to gain support among the lords of Westeros, perhaps using his charm or military prowess. But without more details from the books or other official sources, we can only guess at his significance.
One interesting fanfiction could be about Lysa Arryn's early life in the Vale before the events of the series. It might explore her relationship with her family and how it shaped her into the character we see in the show. Another could be a what - if scenario, like what if Lysa Arryn had allied with a different house instead of the Lannisters. There are also fanfictions that focus on her relationship with Littlefinger in more depth, showing the manipulations and her emotional turmoil in that relationship.
The 'Game of Thrones' world is vast and full of possibilities in fanfiction. Regarding Jon Arryn's wife in a Blackfyre - related fanfic, it's likely that the fanfic author has crafted a unique story. It could be that the wife is a character who is a part of a secret Blackfyre plot, or she might be a noblewoman from a house that has some connection to the Blackfyre legacy. However, without actually delving into the fanfic, we can only speculate about who she might be.
In the fanfic, she could be a key figure in a political plot. Maybe she has some connection to the Blackfyre claims which could influence the power dynamics in the story.
One popular fanfic in this vein is 'The Arryn - Targaryen Alliance'. It delves into the political implications of such a union. The story weaves a complex web of court intrigue as Jon Arryn's Targaryen wife tries to navigate the power - hungry world of Westeros. It's well - written and has some great character development.