A delinquent pulling a baby demon king out of a river and being told he has to raise it is the kind of premise that only works if you commit to it completely, and this special commits. The comedy lands because it treats supernatural chaos like a normal Tuesday at a school full of thugs. If you've read ahead in the manga, this hits different, it's a celebration of what's coming, not an introduction.
Oga Tatsumi holds the reputation of being Ishiyama High's most fearless delinquent, a guy who settles every problem with his fists and asks questions later. That changes when he fishes a mysterious man out of a river, only to watch him literally split apart and reveal a baby inside. Not just any baby: this is the infant son of the demon king himself, and according to the maid Hilda who materializes alongside him, Oga has been chosen as the child's caretaker whether he likes it or not. What should be a disaster becomes something stranger. Oga finds himself balancing the chaos of raising a demonic prince with attending a school full of violent punks who'd love nothing more than to test his strength. The baby, called Beelzebub, has inherited his father's power in miniature form, meaning trouble follows wherever he goes. Between protecting the kid, dealing with increasingly absurd situations at school, and figuring out why he was picked for this insane job in the first place, Oga's already chaotic life spirals into complete pandemonium.