Perhaps a fanfiction where Jon Snow is wrongly accused of a crime in King's Landing. Robert Baratheon, known for his sense of justice (at least in some aspects), decides to investigate the matter himself. As he delves deeper, he discovers that Jon is a far more complex and noble character than he initially thought. This could be the start of a friendship or a mentor - mentee relationship between them, with Jon teaching Robert about the harsh realities of the North and the Wall, and Robert teaching Jon about the politics of the South.
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.
In a fanfiction, the plot could be that there is a prophecy that involves both Robert Baratheon and Jon Snow. They are brought together by a seer or a maester who has uncovered this ancient prophecy. They initially don't trust each other, but as they learn more about the prophecy and its implications, they realize that they must work together. Their journey could involve traveling to different parts of Westeros, facing various challenges and enemies, all while trying to fulfill the prophecy and save the Seven Kingdoms from a great threat.