Caspian X’s uncle who rules Narnia as a usurper is Miraz.
Miraz is the Telmarine king who seizes power after murdering his brother, Caspian IX. He initially tolerates his nephew, Prince Caspian, because Caspian is the heir, but turns against him when Miraz’s own son is born. Caspian flees the court and seeks help from the Old Narnians.
In Prince Caspian, Miraz’s rule represents the Telmarine suppression of Narnia’s talking animals and mythical peoples. Peter eventually challenges him to single combat, with the battle intended to decide the wider conflict. Miraz loses, but his supporters Glozelle and Sopespian accuse the Narnians of cheating and trigger a general attack.
Miraz is ultimately stabbed in the back by Glozelle during the confusion. Sopespian and Glozelle are his political allies, not the usurping king himself; Rabadash belongs to the separate Calormene storyline in The Horse and His Boy.