Biography
An evil character who appears to be a satanic figure for the setting, although they clearly aren't the Devil himself.
A Satanic Archetype character can be any combination of the following:
A tendency for entering bargains with the intent of helping the other person in the short term, but screwing them over in the long term. If portrayed as more of a Noble Demon then said Satanic character might not intend to do more than what's in the contract — but they will still exact their pound of flesh from anyone who fails to uphold their end of the bargain.
A Fallen Angel who rebels against the creator's will, and may or may not want to supplant them. If there are no beings outright called angels in the setting, then said character could be a member of another group of beings who were either divine, otherworldly, or just have abilities that others don't. Bonus points if they were their creator's favorite pre-fall.
A tempter, who guides decent people towards indecent things. Often an Evil Mentor or a toxic friend, sometimes more supernatural and less corporeal.
A God of Evil.
A ruler of demons, or devils.
Something that looks the part.
Embodies most or all of the Seven Deadly Sins.
Is known by various names, has many faces and is called many things.
Is associated with animals that are considered dark or malevolent (like wolves, dragons or snakes).
May or may not have fire powers or dark powers (because demons and hell are often associated with fire and/or darkness).
Alternatively to the powers, they may invoke the literal meaning behind Lucifer - "bringer of light" - and be strongly associated with light and colors associated with both brightness and beauty, especially if they are also a Narcissist. Expect a Red Right Hand or a menacing One-Winged Angel form, though.
Chances are, if a work is using Everybody Hates Hades, then Hades or another being or creature associated with death will be depicted as a Satanic Archetype. If the character lampshades their own satanic qualities, then it falls under Devil Complex.
Super-Trope of Davy Jones. See also The Trickster, Hijacked by Jesus, God of Evil, The Anti-God, Maou the Demon King, Classic Villain, Southern Gothic Satan (a Deep South version of Satan), Louis Cypher (a trope which frequently overlaps with this one) and Demiurge Archetype (who impersonates God rather than going head-to-head against Him) Contrast with Crystal Dragon Jesus, Madonna Archetype, Messianic Archetype, Moses Archetype, Big Red Devil (who looks Satanic but doesn't necessarily act the part). Tends to share traits with the King Koopa Copy.