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.
In a Naruto - Lannister Game of Thrones fanfiction, the story could start with Naruto being transported to the Game of Thrones universe and adopted by the Lannisters. Naruto's sense of justice would immediately clash with the Lannisters' self - serving ways. For example, he would not stand for the way they treat the smallfolk. He might try to use his ninjutsu to improve the lives of the common people, which would draw the ire of other power - hungry nobles. His relationship with the other members of the Lannister family would be complex. He could befriend Tyrion, who also has a sense of justice that is often suppressed. However, characters like Cersei would see him as a threat to her power and try to eliminate him.
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.
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.
Naruto would probably be a bit of an oddity at first. He's used to the shinobi world, so the politics of Westeros would be really strange to him. But he'd be his usual energetic self. He might see the Baratheons as a sort of new 'clan' to be part of. He'd likely try to bring his sense of honor and protecting the weak to the Baratheon court.
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.
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.
Well, perhaps the magic in 'Game of Thrones' could be related to the advanced technology of Atlantis. For instance, the wizards in Westeros might be seen as having a similar power source as the Atlantean crystals or something. It could make for a really cool story where the two worlds' power systems are intertwined.
In a Naruto - Game of Thrones crossover fanfiction, the story could start with Naruto being transported to Westeros. He would be confused by the different political system and the lack of chakra. But he would soon adapt. He could form an alliance with the Starks, teaching them some of his ninja techniques in exchange for their protection. His positive attitude towards life would be a contrast to the often dark and cynical world of Game of Thrones.
One great 'Game of Thrones OC Baratheon fanfiction' is 'The Baratheon Heir'. It has an interesting plot where the OC Baratheon character tries to reclaim the family's lost glory in a really engaging way.
To develop a male OC Baratheon, start with his physical appearance. Maybe he has the typical Baratheon black hair and blue eyes, but with a scar on his face from a battle. Then think about his personality. He could be proud like most Baratheons, but also have a sense of humor.