Arya Stark could be an ally. She has her own set of skills and could work with Jon Snow on the back of the dragon for strategic attacks. For example, Arya could use her stealth to infiltrate enemy camps while Jon provides air support with the dragon.
Tyrion Lannister could also be an ally. His intelligence and strategic mind would be valuable. He could help Jon Snow plan battles and manage the politics that come with riding a powerful and feared creature like a dragon.
Daenerys could be an ally. Since she is the mother of dragons, she might initially be hesitant but then see the potential in Jon Snow riding one of her dragons. They could team up to fight their common enemies.
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.
His main allies could include Davos Seaworth. Davos is a shrewd man and has a lot of experience in the political games of Westeros. He could offer Jon advice on how to navigate the court. Another possible ally could be Brienne of Tarth. She is a skilled warrior and shares Jon's sense of honor. They could fight side by side to protect the king. Also, Gendry could be an ally. He has his own strength and could be useful in battles to defend the king.
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.
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.
His half - sister Sansa would likely be one of his allies. She has proven herself to be a shrewd politician and would be a great asset in ruling the Seven Kingdoms. Also, the North would most probably stand by him, considering he is a Stark.
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.
In a fanfic where Jon Snow rides a dragon, he would gain several new abilities. The ability to fly, of course, is a major one. This would allow him to have a better view of the battlefield, plan strategies more effectively. The dragon's fire could be used to burn down enemy fortresses or large groups of foes. Also, the dragon itself is a symbol of power, so Jon would gain more respect and fear from others. He could intimidate his enemies just by showing up on his dragon. Moreover, the bond with the dragon might give him some kind of telepathic connection, enabling him to control the dragon more precisely.
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.
Daenerys Targaryen is a very likely candidate. Their connection through their Targaryen blood (Jon's true heritage) could be a strong basis for a marriage. They could join their forces, both having a claim to the Iron Throne, and rule Westeros together. Their marriage would also symbolize the unification of the North and the South, as well as the different Targaryen branches.
Well, the dragon would obviously be a main character in its own right. It could have its own personality and motives.