See on Act 24:5. The word is commonly used in an indifferent sense, as signifying merely a school or party. So Act 15:5; Act 28:22. Here, however, in a bad sense - schismatic sect, as in 1Co 11:19.
Worship (λατρεύω)
Better, as Rev., serve. See on Luk 1:74.
God of my fathers (τῷ πατρώῳ Θεῷ)
A familiar classical phrase, and therefore well known to Felix. Thus Demosthenes calls Apollo the πατρῷος (ancestral god) of Athens. Socrates is asked (Plato, “Euthydemus,” 302), “Have you an ancestral Zeus (Ζεὺς πατρῷος)?” So, frequently, in the classics. Similarly, the Roman phrase, Di patrii, “the gods of the forefathers.” On the Roman reverence for the ancestral religion, see note on Act 16:21. The Roman's own sentiment would prepare him to respect Paul's.