Strengthened from a primary tegos (a "thatch" or "deck" of a building); a roof -- roof.
Thayer's Greek Lexicon
Strong's 4721: στέγη
στέγη, στεγης, ἡ (στέγω to cover), from Aeschylus and Herodotus down, a roof: of a house, Mark 2:4; ἐισέρχεσθαιὑπότήνστέγηντίνος (see εἰσέρχομαι, 1, p. 187{b} bottom), Matthew 8:8; Luke 7:6.
Matthew 8:8 - N-AFS GRK:ὑπὸ τὴν στέγην εἰσέλθῃς ἀλλὰ NAS: under my roof, but just KJV: under my roof: but speak INT: under the roof you should come but
Mark 2:4 - N-AFS GRK:ἀπεστέγασαν τὴν στέγην ὅπου ἦν NAS: they removed the roof above KJV: they uncovered the roof where INT: they removed the roof where he was
Luke 7:6 - N-AFS GRK:ὑπὸ τὴν στέγην μου εἰσέλθῃς NAS: for You to come under my roof; KJV: under my roof: INT: under the roof of me you should come