One common theme is the struggle for power. Jon has to face those who oppose his claim to the throne. Another theme is identity. Discovering he is the heir makes him question who he really is.
Well, it really depends on what you're looking for. There are fanfictions that focus on the political intrigue that follows when Jon's claim is revealed. Others might be more about his relationships with other characters in the context of being the heir. I'd recommend searching on platforms that have a large Game of Thrones fanfiction community and reading the reviews to find the good ones.
Power struggle is a very common theme. The heir often has to fight against other claimants or those who want to usurp the throne. Another theme is self - discovery. The heir has to figure out their own identity and capabilities as they are groomed for the throne.
A great deal of Jon Snow and Iron Throne fanfictions focus on his relationships. For example, his relationship with Daenerys could be very different in fanfictions. In some, they rule together on the Iron Throne, combining their claims and powers. In others, they are at odds, with their relationship being a major obstacle in Jon's path to the throne. And of course, there are fanfictions where his Stark family ties also influence his actions regarding the Iron Throne, as loyalty to his family is a strong part of his character.
One ending could be that Jon Snow ascends the Iron Throne alone. He has proven himself as a leader, defeated his enemies, and is seen as the rightful king. This ending might show him ruling with justice and mercy, much like how he was in the original series. Another ending could be that he refuses the throne. After all the chaos and bloodshed, he realizes that power is not what he wants and instead chooses to go back to the Wall or live a simple life in the North.
In a 'Jon Snow sits on the Iron Throne' fanfiction, Jon might start by reforming the way the throne is perceived. Instead of it being a symbol of power and fear, he could make it a symbol of unity. He would have to make tough decisions regarding the remaining White Walkers threats, if any. Also, his relationships with other characters like Daenerys' followers would be very interesting to explore as he tries to bring stability to the Seven Kingdoms.
Well, in a 'Jon Snow takes the Iron Throne' fanfiction, perhaps Jon discovers some long - lost magic or prophecy that gives him an undeniable claim to the throne. He has to fight off some last - ditch attempts by his enemies to stop him. Once on the throne, he might start a new era of peace by making alliances with former foes. He could also start to rebuild the parts of Westeros that were destroyed during the wars, using the resources and manpower available to him in a smart way.
The North would surely support him. They have always seen him as one of their own and a great leader. Also, the wildlings might back him, considering he has a history of working with them and understanding their plight. Davos Seaworth would most likely be on his side as well, given his loyalty to Jon in the past.
Well, perhaps there's a plot twist where they take the Iron Throne but then realize it's a false victory. There could be a shadowy organization behind the scenes that has been manipulating events all along. This organization could then try to undermine their rule. Also, what if the throne itself has some sort of mind - controlling power? It could start to influence Jon and Daenerys in unexpected ways, leading to a rift between them.
Their relationship could become strained as they face the challenges of ruling. They might have different ideas on how to govern Westeros, which could lead to arguments.
Love and romance can also be a theme, not just in a romantic sense between them but also their love for their family, the North, and their people. And of course, there's the theme of survival. They both have to survive in a very harsh and dangerous world, and fanfictions show how they do that, sometimes relying on each other and sometimes on their own wits.