From Middle Dutch stief-, stiep-, from Old Dutch *stiop-, from Proto-West Germanic *steupa-, from Proto-Germanic *steupa- (“bereft, pushed out”).
Cognate with German stief-, English step-. The form with -f- arose through assimilation before the word vader (“father”); the generalization of this form may or may not have been reinforced by High German influence (where the -f- is regular). Compare the same in Middle Low German stêf-.