Lit. after the manner of Isaac. See Rom 9:7-9, and, for this use of κατὰ, 1Pe 1:15; Eph 4:24; Col 3:10.
Children of promise (ἐπαγγελίας τέκνα)
Not promised children, nor children that have God's promise, but children who are not such by mere fleshly descent, as was Ishmael, but by promise, as was Isaac: children of the Jerusalem above, belonging to it in virtue of God's promise, even as Isaac was the child of Sarah in virtue of God's promise.