While Castlevania III is a largely linear experience focused on reaching Dracula, its branching paths and character recruitment mechanics offer a form of 'side content' by encouraging multiple playthroughs. There aren't traditional side quests in the modern sense, but there are distinct paths and hidden items that reward exploration.
The primary 'side activity' is exploring all possible routes to recruit each of the three allies: Sypha, Grant, and Alucard. Each playthrough with a different combination of allies will feel unique, offering varied strategies and challenges. Additionally, finding all the whip upgrades and maximizing your sub-weapon potential can be considered a form of progression beyond just beating the game.
Compare side quests & activities inCastlevania: Portrait of Ruin