In Birth by Sleep, Master Xehanort’s masked apprentice is Vanitas.
Vanitas is one of the game’s principal antagonists and serves Master Xehanort’s plan to create the χ-blade. His identity and origin are tied directly to Ventus: Xehanort extracted darkness from Ventus’s heart, giving that darkness a separate form. The resulting figure became Vanitas.
Vanitas wears a mask and initially conceals his face, helping preserve the mystery surrounding his connection to Ventus. His name also echoes Ventus’s, and his later resemblance to Sora is explained by the connection formed between Ventus’s heart and the newborn Sora.
Braig is another important figure in the story, but he is not Xehanort’s masked apprentice. Terra is one of the three playable protagonists, while Marluxia belongs to the later Organization XIII storyline. Vanitas’s role is therefore the single canonical answer.