In this fanfiction, one of the key battles Jon Snow might participate in could be the Battle of the Whispering Wood. His skills as a fighter would be put to good use there, sneaking around and taking out enemies. Another could be a fictional battle near the Wall, where he defends against some new threat that has emerged during Robb's war.
In this fanfiction, Jon Snow's character could develop in several ways. Firstly, his relationships with other characters might change. He may form stronger bonds with his fellow soldiers, learning to trust them more. Secondly, his understanding of politics and power could grow. As he is involved in Robb's war, he witnesses the political maneuverings that go on behind the scenes. This could make him more cynical or more determined to fight for justice, depending on how he interprets these events. Moreover, his combat skills are likely to improve, and this newfound strength could give him a different perspective on his own capabilities and his place in the world.
The wildlings might be his allies. After all, Jon Snow has had interactions with them before. They are fierce fighters and could fight alongside him against a common enemy.
Well, it could be about Jon Snow leading his men into a great battle against the White Walkers. Maybe he discovers new strategies or forms unexpected alliances during the war.
Survival is also a common theme. In the midst of the chaos of the War of Five Kings, Jon Snow has to fight to survive, both physically against enemies and politically in a world full of backstabbing and power - hungry people. Also, the theme of identity. He is a bastard, but in these fanfictions, he often has to define himself beyond that label, especially during the war.
Jon Snow could potentially have allies like the Mormonts. They have always been loyal to the Starks. Maybe even some of the Dornish houses might side with him. They have their own reasons to oppose the current power structure in Westeros. And of course, his friends from the Night's Watch who left with him or believe in his cause could be his allies in this conquest. He might also gain the support of some of the maesters who see the value in his leadership for the future of Westeros.
Daenerys Targaryen could be one to help. Since she has experience with dragons, she could give Jon Snow advice on how to care for the egg and hatch it.
It could be a young and untainted Frey. Maybe a niece or a cousin of the more infamous Freys. One who has not been involved in the past atrocities committed by her family and has a more noble heart.
Daenerys Targaryen is often paired with Jon Snow in such fanfictions. Their combined power and the potential for a different kind of relationship makes it a popular choice among writers. Another character is Arya Stark. Their sibling bond can be explored in new ways when Jon is reincarnated, like Arya helping Jon with her assassin skills in a different plot line.
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.