Sure. There are quite a few out there. Many fanfiction writers are attracted to the idea of bringing together characters from different eras of the Game of Thrones universe, like Jon Snow and Rhaenyra Targaryen. These stories often play with the Targaryen heritage and the different powers and personalities of the two characters. For example, a fanfic could focus on how Rhaenyra's experience as a claimant to the Iron Throne might influence Jon's own understanding of leadership and power.
The common themes include the struggle for power. Rhaenyra's struggle for the throne and Jon's battles in the North both revolve around power. Fanfictions may have them collaborate or compete in power - related scenarios. Another theme is the clash of different cultures. Jon grew up in the North, which has its own culture, while Rhaenyra was a part of the Targaryen - dominated court. Their interactions in fanfiction can highlight how these different cultures mesh or clash. And the mystery of their Targaryen lineage can also be a central theme, with fanfictions delving into the secrets and powers that come with it.
In addition to Jon and Daenerys, other characters might also play important roles in some fanfictions. For instance, Tyrion Lannister could be there as an advisor to Daenerys. His wit and political acumen might help in the interactions between Jon and Daenerys. Or Arya Stark could be involved in some way, perhaps as a spy or a messenger between the North and Daenerys' camp. These additional characters can add more depth and complexity to the story of Jon and Daenerys' meeting.
Another plot could be that they meet under very different circumstances. For example, Jon is sent as an emissary to Daenerys much earlier in the story. At first, Daenerys is skeptical of Jon's claim to the North and his intentions. However, as they spend time together, they discover a shared history of their families and a mutual desire to make Westeros a better place. This discovery leads to a strong bond between them, and they start planning strategies to reshape the political and power landscape of Westeros together.
One idea could be that the baby is born with a special ability, like being able to communicate with dragons even more so than Daenerys. Maybe the baby's presence unites the remaining kingdoms in a way that Jon and Daenerys alone couldn't. Another thought is that the baby becomes a symbol of hope for a new era, with people from all over coming to see the new heir of the Targaryen - Stark line.
Allies could include the remaining Stark family members. They would surely support the baby as it is part Stark through Jon. The Unsullied might also be allies as they were loyal to Daenerys. As for enemies, Cersei's remaining supporters could be a threat, seeing the baby as a rival to any power they might still hold. Also, the Night King's followers (if any still exist) could see the baby as a new target, a symbol of the new life they oppose.
I really like the fanfic 'Jon Targaryen: Fire and Ice Reborn'. It shows Jon not only as a powerful Targaryen but also as a character who is trying to balance the power of his dragon blood with his Stark upbringing. The author does an excellent job of creating new storylines that still feel true to the original 'Game of Thrones' world.
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.
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.
The allure of 'Game of Thrones Jon Targaryen Fanfic' also lies in the world - building aspect. The 'Game of Thrones' universe is vast and complex. When Jon is revealed as a Targaryen, it opens up a whole new world of possibilities for fanfic writers. They can create new kingdoms, new battles, and new alliances centered around Jon's newfound identity, which is really appealing to fans of the series.