Some fanfictions about Robert Baratheon might involve his adventures before he became king. For example, he could be on a quest to prove himself worthy of the throne. In another fanfic, he might be in a situation where he has to team up with his enemies to fight a greater threat, like the White Walkers. There could also be a fanfiction that delves into his love life, not just with Cersei but other possible relationships he could have had if things were different in his life.
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.
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.
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.
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.
To make a fanfiction about Robert Baratheon interesting, you can give him new challenges. Maybe he has to deal with a magical threat that the original series didn't show him facing. You could also explore his backstory more. What was his life like before he became king? His upbringing, his first loves, and his early battles could all be interesting areas to explore. Additionally, changing the power dynamics around him can be great. For instance, if some of the minor houses suddenly become more powerful and he has to negotiate with them. This can lead to all sorts of interesting political intrigue and character development.
Another aspect that fanfictions often explore is her relationship with other members of the Baratheon family. In some stories, she could be at odds with Cersei, seeing through her false charm and manipulative ways. This creates a power struggle within the family, which is a common and engaging theme in Game of Thrones fanfiction.
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.
She could also be shown as a great warrior in certain fanfictions. Despite the norms of the society in Game of Thrones that often restrict women's roles in combat, she breaks free from those constraints. She trains in secret and then emerges as a surprise defender of her family when they are under attack.
Another plot could revolve around her discovery of a long - hidden family secret. Maybe she finds out that there is some hidden claim to the Iron Throne within her family's past. This could lead her on a journey to uncover the truth, facing many obstacles along the way, including those who want to keep the secret buried. She might have to outwit her own family members who fear the consequences of this secret getting out.
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.