In this fanfiction, Naruto as the son of Robert Baratheon could introduce the concept of chakra to Westeros. This new form of energy could change the balance of power in the land. He might train a group of loyal followers in the ways of the ninja, creating a new force that could either protect the kingdom from external threats or even become a threat to the existing power structure, depending on how the story unfolds.
Perhaps the story could focus on Naruto growing up in the court of King's Landing. He would face the political intrigue there, which is very different from the world he knew in the Naruto series. His ninja training might give him an edge in dealing with the backstabbing and power - hungry nobles, while also trying to understand his new identity as Robert Baratheon's son.
His abilities might be a blend of his ninja skills and the more 'mundane' skills expected of a noble in Westeros. For example, he could use his shadow clone jutsu to attend multiple court meetings at once, while also learning how to joust or fight with a sword like a true Baratheon.
Perhaps their relationship begins with curiosity. Daenerys has heard of the powerful Robert in Westeros, and Robert is intrigued by this Targaryen with a claim to the Iron Throne. As they communicate more, they find common ground in their desire for a just Westeros. They might start to fall in love slowly as they share their dreams and fears, and work towards building a better future for the Seven Kingdoms.
One great fanfiction could be about the Oc Son of Robert Baratheon trying to claim his rightful place in the Iron Throne. Maybe he has to face off against his siblings or other claimants. It could explore his character development as he discovers the truth about his father's actions and how it affects his own claim.
If Robert Baratheon married in fanfiction, it might result in new alliances and conflicts. His choice of partner could shape the political landscape and introduce fresh storylines. Also, it could affect his relationships with other characters in unexpected ways.
If Robert Baratheon married Cersei in fanfiction, it's possible that their children's fates would be different. Also, it might affect the alliances and rivalries among the noble houses. The story could take many unexpected turns based on this alternate setup.
A plot could be that Robert Baratheon, in his later years, starts to question the legitimacy of the current power structure. He meets Jon Snow, who has a mysterious allure about him. They start to exchange ideas about honor and leadership. Robert realizes that Jon has a different kind of wisdom, born from his experiences at the Wall. This leads to a journey together where they try to find a new way to rule the Seven Kingdoms that is more just and inclusive.
It could have led to a very different power dynamic in Westeros. Maybe Robert would have been more controlled by Cersei, or their relationship could have sparked more political upheaval.
Good fanfiction about Robert Baratheon also needs to capture the essence of the world he lives in. It should include the political intrigue, the power struggles, and the cultural aspects of Westeros. If it can tie in his actions as king with the greater political landscape, like how his decisions affected the different houses, it makes for a great read. Also, delving into his vices, like his drinking problem, and how it impacts his rule and those around him is a plus.
Power is a common theme. Fanfictions often explore how Robert wields his power as king, whether he uses it wisely or misuses it. Another theme is love and lust, like his relationship with Cersei and how that affected his rule.
One idea could be a fanfiction where Robert Baratheon's son, perhaps Joffrey (even though he was a cruel character), has a change of heart. In this fanfic, he could start to see the error of his ways after meeting a wise old maester who tells him tales of great but just kings. He then tries to make amends for his past actions, which would be a huge departure from his original character arc in the show and books.