One possible fanfiction could start with Robert Baratheon as a young man. He is full of ambition and dreams of a united Westeros under his rule. He trains hard in combat, his sword becoming an extension of himself. He meets his future friends, like Ned Stark, during these formative years. They share tales around the campfire and make grand plans for the future. As he grows older, he participates in battles, his victories making him more and more renowned. His charisma draws people to him, and soon he is seen as a natural leader. But with power also comes temptation, and he has to face the challenges of politics and intrigue that come his way.
One interesting fanfiction could be one where Renly Baratheon survives and forms a different alliance. Maybe he teams up with the Starks against the Lannisters, which would completely change the power dynamics in Westeros.
Love and loyalty also feature prominently. An OC Baratheon might be torn between loyalty to their family and their love for someone from another house. This creates a lot of internal conflict and interesting plotlines. In some stories, an OC Baratheon's loyalty to a friend or a romantic partner can change the course of events in the political landscape of Westeros.
One interesting fanfiction could be one where Robert Baratheon survives and has to face the challenges of ruling Westeros in a more peaceful way. He might have to deal with political intrigues without the use of brute force as much. Another could be a story about his youth, exploring his relationship with Ned Stark before all the chaos of the Iron Throne began. And there could also be a fanfic that focuses on his relationship with his children, had he been more involved in their upbringing.
There might be a fanfiction where Tommen discovers a hidden power within himself. For example, he has the ability to communicate with animals. This new power helps him to better understand the needs of his people and make more informed decisions as king. He could use this power to gain the loyalty of his subjects in a unique way.
Well, one way could be through a magical portal. Imagine Naruto, with his ninja skills, suddenly appears in the world of Westeros. His abilities like shadow clones could be mistaken for some dark magic in the Game of Thrones universe. He might team up with the Baratheons, perhaps using his skills to help them in battles, especially against the White Walkers if we're thinking of a scenario where he arrives during that threat.
The male OC Baratheon could also be a bastard son who has been living in exile. He returns to Westeros with a group of loyal followers he has gathered over the years. His main goal could be to claim a small piece of land for himself and his men, but he soon realizes he has to navigate the complex web of politics and allegiances in order to survive.
Some fanfictions might focus on an alternate universe where Joffrey is not a king. He could be a simple knight, and the story could explore how his personality would develop without the power and privilege of the throne. He might learn humility and honor in a different way.
You can start by looking on fanfiction websites like Archive of Our Own (AO3). It has a large collection of 'Game of Thrones' fanfictions, and you can specifically search for ones related to Robert Baratheon. Another option is FanFiction.net. There are many writers on there who might have created interesting stories about him.
One idea could be an OC Baratheon who is a long - lost cousin. This OC could come to King's Landing with a claim to the throne, causing political unrest among the existing Baratheon claimants. He or she might have unique skills, like being an expert in naval warfare, which was important for the Baratheons. Another plot could involve an OC Baratheon woman who disguises herself as a man to fight in the wars, and along the way, she discovers secrets about her family's past that could change the course of the Baratheon legacy in Westeros.