His father was Gaius Septimus. While Tavi was still an infant, Isana used her fury to slow Tavi's growth so that his identity as heir to the throne could be hidden. Later, it's seen that Tavi suddenly has the power to furycraft when he accidentally turns off a furylamp.

Does Tavi have a fury?

Ok so Tavi hasn't manifested any furies yet. He hasn't found a fury that is attracted to him.

Is Tavi Gaius grandson?

In Book 5 of the Codex Alera series, young Tavi of Calderon, recently outed as Gaius Octavian—the grandson of Alera's ruling First Lord Gaius Sextus, and thereby Princeps of the realm—faces a crisis in which the antagonistic races that populate his world must either come together or perish separately.