I am not gonna go through my usual review table, but instead, straight up, tell my thoughts for this story. But my review is just criticism for the story, and hopefully, the author can grow from this.
So first, for writing quality, it gets 2 stars. The reason I gave it this is because the grammar is fine and passable, but I do not like the transition at all. It felt very annoying with the transition of the timeskip to another it wasn't a smooth one at all. In fact, it was very incredibly annoying, especially with how quickly everything fell into place.
I also didn't understand Daemon characters in the story whatsoever. To me, it never made sense how much why he disliked Aemon. I know it's your version of Daemon, and that's fine, but in my personal opinion, Daemon is not this much of a pain towards his own child, especially a son. He has a view of Targaryen supremacy, but the fact that his son had a dragon should mean that he is proud of him, especially since he looked more Valyrian than Royce. It's been stated that the MC looks like Aemon Son of Jaehaerys rather than a Royce.
Viserys disliking him early in his childhood doesn't make sense also, why would he be jealous of his grandmother liking his grandson more. Isn't it like that for every old person who has grandchildren. I think he would've appreciated Aemon more. Lastly, his disinheritance of the line is just stupid. It wouldn't matter if he was Daemon's child. He would've been looked upon as a still favorably, especially as a Dragon rider and someone who was greatly cared for by Alysanne. It genuinely never made sense to me.
Aemon is fine playing passive, but the way you just skimmed over the details is really annoying, but I get you want to go ahead and do the dance. I don't really like your depiction of Rhaenyra. Sure, Daemon could've influenced her to think that way, but her mother was an Arryn. She was raised more by her mother than her father. It doesn't matter if her maternal grandmother was a Targaryen. She is basically one-quarter Targaryen. With Aemon just being half, he had a bastard who is basically the same thing? Daemon is someone who hates people who don't look Targaryen.
Rhaenyra's attitude, especially to someone who is like a year younger than her, doesn't make sense to me. Especially since she was raised by her mother. Sure, she is fierce and immature, but to hate someone you don't know is something she wouldn't do, especially due to her mother and her father being so kind.
Story Development Wise, I gave it a 2 because I genuinely am confused about how this is heading. He is intelligent, but he genuinely doesn't know how to use it that well. He reinforces Runestone, but he doesn't grab more power for himself in the Arryn? It doesn't feel like he is doing that. Sure, avoiding the game of thrones will make you live and win. But literally, he has to play it. He is a royal prince. He can't disappear and be forgotten about, especially with a dragon that is capable of being the size of Balerion. It genuinely doesn't make sense that he doesn't play the game. Sure, he avoids it, but I want to see more chapters of him playing it better without being cringe.
The rest are 5 stars because everything is fine except those concepts I mentioned. I feel like you need to work more on flushing out the characters and being more immersed in the world of ASOIAF, I just feel like this is just a regular typical self insert. I know you are writing this as a passion, and that's fine. Keep writing. Don't take my suggestions or my critics too seriously. These are just my opinions. Other than that,keep writing, keep going. Thank you for reading.