A zeal for God (ζηλον θεου). Objective genitive like Philippians 3:9, "through faith in Christ" (δια πιστεως Χριστου).

But not according to knowledge (αλλ' ου κατ' επιγνωσιν). They had knowledge of God and so were superior to the Gentiles in privilege (Romans 2:9-11), but they sought God in an external way by rules and rites and missed him (Romans 9:30-33). They became zealous for the letter and the form instead of for God himself.