A zeal for God (zēlon theou). Objective genitive like Phi 3:9, “through faith in Christ” (dia pisteōs Christou).
But not according to knowledge (all' ou kat' epignōsin). They had knowledge of God and so were superior to the Gentiles in privilege (Rom 2:9-11), but they sought God in an external way by rules and rites and missed him (Rom 9:30-33). They became zealous for the letter and the form instead of for God himself.