Jon Snow could be sent back to a time just before Ned Stark's father was killed. With his future - learned wisdom, he could try to save his grandfather and thus change the entire Stark family's fate. He may also discover secrets about his own lineage that were lost in time. This could lead to him having more power and influence in the past, as he might be able to claim certain rights or titles based on this new - found knowledge.
Jon could find an ally in Arthur Dayne. Dayne was a great knight, and if Jon could prove his worth and show that he has knowledge of threats to come, Dayne might side with him. Also, Bran the Builder is a possibility. Given that Bran is such an important figure in Westeros' history and has some connection to the supernatural, he might be intrigued by Jon Snow's situation and decide to help him in his time - traveling endeavors.
One possible plot twist could be that Jon Snow goes back in time and accidentally changes something that leads to a completely different future for the Stark family. For example, he might prevent Ned Stark from going to King's Landing, which would change the power dynamics in Westeros entirely.
His relationship with his father, Ned Stark, would be different. He could finally have a real father - son relationship instead of the hidden one. He might be able to learn from Ned and become an even better leader in the North.
Regarding his relationships with his friends and comrades, like Samwell Tarly, things would be altered. He might not meet Sam in the same way as before. And his relationship with Daenerys Targaryen could be completely different. Instead of meeting her during the events of the original story, he could meet her when she was much younger, and this could lead to a very different kind of relationship, maybe one that's more of a mentorship or a completely different romantic connection.
Another interesting plot would be if Jon Snow went back to the time when his father, Ned Stark, was a young man. He could interact with his father, perhaps change some small events that had big consequences later. He might also learn more about his family's secrets directly from Ned, things that were lost in time in the original story.
One great 'Jon Snow Time Travel Fanfiction' is 'A Time for Wolves'. It takes Jon Snow back to key moments in Westeros' history, allowing him to change certain events. The story is well - written, with detailed descriptions of the different time periods.
A major theme is the preservation of the future. In many Jon Snow time travel fanfictions, he travels back in time to prevent disasters that would lead to the downfall of Westeros in the future. Another common theme is the exploration of different cultures within Westeros. Since he can travel to different time periods, he gets to experience and interact with various cultures that may have been long - lost or changed in his own time.
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.