Where does “demonic” come from?

Demonic comes from Latin daemonicus, from Ancient Greek δαιμονικός, from δαίμων, from δαίομαι, ultimately from Proto-Indo-European -mō.

demonic (English): Pertaining to demons or evil spirits; demoniac;...

Definitions

Step	Language	Word	Meaning
1	Latin	daemonicus	demonic, devilish
2	Ancient Greek	δαιμονικός	possessed by a demon, sent by a demon
3	Ancient Greek	δαίμων	god, goddess; departed soul; demon, evil spirit
4	Ancient Greek	δαίω	to light up, to kindle, to set on fire; to burn...
5	Proto-Indo-European	deh₂y-	to share, divide
6	Proto-Indo-European	deh₂-	to share, divide