A devil-child movie is a type of horror movie where the antagonist or anti-hero is a child or child-like demon or child possessed by an evil force or something similar. For example, Rosemary's Baby was about a woman who sells her baby to a witches' coven; the effect makes the viewer think: "Don't have this baby; abort it!"
Many such movies were made in the years 1960-1984, which was precisely when Generation X was being born.
A Brief Chronology of the Devil-Child Movie Era: