Political schemes and internal division among his family and the ruling houses of Westeros led to Aegon inheriting the Iron Throne and becoming king of the Seven Kingdoms instead of his elder half-sister Rhaenyra
According to both accounts, Aegon did not want to be king but was convinced by Criston, who stressed that should he refuse the crown, Rhaenyra would kill Aegon, his siblings, and his children. Ten days after Viserys' death, the prince insisted that he be made king.
Still, Aegon gets ultimately crowned as Aegon Second of His Name, King of the Andals and the Rhoynar and the First Men, Lord of the Seven Kingdoms, and Protector of the Realm.
Aegon being given the Conqueror's crown, as well as his Valyrian steel sword, Blackfyre, is an effort to further cement his own legitimacy: it's a connection to the person who established the entire Targaryen family dynasty in Westeros and united the Seven Kingdoms under one rule that Rhaenyra simply cannot match.
However, Rhaenyra, dubbed The Half-Year Queen, only sits on the throne for around six months, before she is judged a traitor and forced to flee King's Landing and killed. After which Aegon II reclaims his throne, dying soon after.
Ultimately, Aegon II reigned as king, though he would be succeeded by Prince Aegon the Younger, his nephew by Rhaenyra and Daemon.
As for Rhaenyra Targaryen, she grew up believing she would rule Westeros. But when the time came, her enemies and family stole the crown from her. She answered with fire and blood and was destroyed by them. So while Rhaenyra may have been the first woman to claim the Iron Throne, she never ruled the Seven Kingdoms.
The dripping blood was taken as a sign that the throne had rejected her; her days as ruler would be few. Eustace further claims that Rhaenyra would continuously cut herself more frequently when she sat on the Iron Throne and became more stout from gluttony during her time in King's Landing.
George R. R. Martin's Fire and Blood book reveals several reasons for this approach from House of the Dragon. Firstly, Rhaenyra has a purer Targaryen bloodline than Aegon, as Viserys' first wife was Aemma Arryn, who was Rhaenyra's mother and cousin to Viserys.
In the end, Aegon fed his half sister to his dragon, and it is said that Sunfyre only reacted to Rhaenyra after her breast was pricked by Alfred's dagger, with the smell of her blood rousing the dragon.
With both Rhaenyra and Aegon gone, there's one clear person to inherit the throne: Rhaenyra's son Aegon, known as “Aegon the younger” in the books (her older sons had all died by this point).
Obviously, Aegon and Rhaenyra are enemies fighting for the throne but at the end of the day, they are siblings.
She and her husband Daemon have a child named Aegon, his full name being Aegon Targaryen. Rhaenyra chose this name in order to further support the legitimacy of her claim to the crown. After all, she's the mother of the boy who bears the name of the greatest king the realm has ever known.
With no one left to help her, Aegon II demanded his dragon Sunfyre to kill and then consume his older sister right in front of the eyes of her last remaining child and future king, Aegon The Younger.
Viserys II Targaryen was the tenth Targaryen king to sit the Iron Throne as Lord of the Seven Kingdoms. He was the son of Rhaenyra Targaryen and Daemon Targaryen, the brother and Hand of King Aegon III Targaryen, and the father of King Aegon IV Targaryen, Queen Naerys Targaryen, and Prince Aemon "the Dragonknight".
It is you. You are the one. You must do this. You must do this." In many ways, for Rhaenyra who has always felt the pressure of the realm preferring her younger half-brother over her, this would have been a solid confirmation that even in his last moments, Viserys does not regret naming her as his heir.
Viserys also shares a secret with Rhaenyra, one that she must hold with her, and it's pretty big. He reveals that Aegon Targaryen, the first king to sit on the Iron Throne, foresaw the end of mankind.
His legendary ancestor, King Aegon the Conqueror, had a vision that the world of men would fall, and understood that only his family of Aryan inbreds could save it. Viserys tells his daughter, Princess Rhaenyra, that Aegon “foresaw the end of the world of men.
According to the accounts of Septon Eustace, prior to her turning sixteen, Rhaenyra lost her virginity to her uncle, Prince Daemon, after he seduced her.
Joffrey Baratheon spoils Rhaenyra Targaryen's fate on Game of Thrones. As Joffrey tells us, eventually, Rhaenyra's half-brother Aegon Targaryen will feed her to his dragon Sunfyre. She dies as her son, Aegon III, watches. That's the bullet point version.
Rhaenyra's eleven year-old son, Aegon the Younger, was crowned king, and married to Aegon II's daughter and only remaining child, Jaehaera Targaryen, uniting the claims.
Rhaenyra Targaryen, the rightful heir to the Iron Throne, briefly considered bending the knee to her half-brother King Aegon II in the Season 1 finale of House of the Dragon, thus sparing the citizens of Westeros years of dragon fire and bloodshed.
Daemon shows his genuine care and attention to Rhaenyra several times before the two marry. This doesn't take away from the many destructive and inappropriate parts of their relationship, but the books imply that Daemon does love Rhaenyra.
The moment happens in season 3, episode 4, “And Now His Watch Is Ended,” when Joffrey Lannister is chilling with Margaery Tyrell and giddily explains, “Rhaenyra Targaryen was murdered by her brother, or rather, his dragon. It ate her while her son watched. What's left of her is buried in the crypts right down there.”
King Aerys II Targaryen ("The Mad King")
The final undisputed monarch of the Seven Kingdoms from House Targaryen, King Aerys II Targaryen is widely known as the "Mad King" who was usurped by King Robert I Baratheon. Aerys II is a direct descendant of King Viserys I Targaryen through his daughter Rhaenyra.