Castlevania II: Belmont's Revenge
It had been 15 years since Dracula's defeat at the hands of Christopher Belmont, and the land had been relatively peaceful (as much as any land populated by the creatures of Hell can be). Christopher had gotten married, had himself a kid (a son named Soleiyu, poor sod), and watched his son grow into a man.
One day, however, Soleiyu disappeared. That same day, four mystical castles appeared. Fearing somehow Dracula was behind both events, an older, more grizzled Christopher set off to the castles, taking them each on and conquering their masters.
Upon the destruction of the four castles, Dracula's own appeared. As he had before, Christopher fought his way through the demon fortress, battling Dracula's worst fiends. At the top, though, he faced not Dracula, but Soleiyu possessed by the Dark Lord.
Christopher and Soleiyu fought, and the battle raged fiercely, two well trained warriors battling to the death. Christopher won, and managed to banish Dracula from his son's body before he had to kill the teen. Freed of Dracula's presence, Soleiyu told Christopher about Dracula's plans, about how Dracula had escaped from the battle 15 years ago, nearly defeated and forced to rebuild his power. Dracula planned to use the power of the four castle masters to rebuild his body and reclaim his role of lord of the realm.
Knowledge in hand, Christopher fought through the true keep of the fortress, and there fought against a stronger (if not fully empowered) vampire lord. Although Dracula fought as well as he could, Christopher gained the upper hand, defeating the demon and sending him back to the depths of Hell for a time.
The Dark Lord defeated, father and son watched the castle crumble once again. With Dracula dead, the lands returned to their (comparative) levels of peace.
Although not the first direct sequel to a previous title (Castlevania and Castlevania II: Simon's Quest having been the first), this title is one of the few direct sequels in the series.
Although called Castlevania II: Belmont's Revenge, the game is most often called Castlevania Adventure II to show it's sequel status. It's unknown why the Adventure portion of the title was omitted.
Dracula possesses Soleiyu, using the child as a vessel. This is another instance of this happening, where he uses a young person to serve as a vessel for his own resurrection. One could assume that, given enough time, Dracula would have fully possessed the teen, taking over his body completely.
The game refers to the fact that Soleiyu would have his own battles with Dracula, but no game was ever made starring the lad.