Dante's Inferno, while playing a big role in weaving the mythological tapestry of hell, has some odd depictions of the devil that haven't really made it into modern popular mythology. Satan, in the Comedy, is a three-headed beast with much of his body encased in ice. He has six wings that eternally flap, only serving to stir up frigid winds and freeze himself further. His three mouths constantly chew on Judas, Brutus, and Cassius - fellow betrayers - and he never says a word.

Dante's Satan is more of a cosmological construct than a character, meant to serve as an opposite reflection of God - trapped in the center of the earth, engaged in endless futility, and fundamentally infertile (Satan, notably, does not have genitalia). Whereas God inhabits the outermost sphere, is utterly free, and is the essence of creation and fertility.

Paradise Lost's Satan is more similar to modern depictions. He's an incredibly eloquent tempter and trickster, and (in my opinion) by far the most compelling character in the epic. That said, Lost still isn't the origin of modern Satan, if what you're talking about is the red-skinned, pitchfork-wielding goat-man.

You may also be interested in this thread, which asks a similar question. This other thread zeroes in on the pitchfork/trident, and produced one of my favorite /r/AskHistorians answers of all time.

There's actually a ton of influence from the outside world in terms of Christianity. There's a large impact from Zoroastrianism, as well as some ideas coming from Gilgamesh, Egypt, and Canaan. Here's a quick, brief breakdown:

Egypt: though this ancient religion believes in multiple "gods" it is actually many manifestations of one God. On that note, the manifestations most closely associated with evil were Seth and Horus. Seth typically was depicted as having a snout, being tall, and was often the color red (the color of the scorching desert sand that would ruin crops). This is where it is assumed the devil got his red hue from. However, Seth is not 100% evil, as the west thinks of the devil.

Mesopotamia & Gilgamesh: most of what we have of these beliefs is from this story. Huwawa is the evil forest monster that breathes fire and death. Gilgamesh and his pal Enkidu go to this forest for whatever reason, and Huwawa tries to attack them, but Gilgamesh ultimately wins. This is the basis of good vs evil.

Canaan: if you know much about Christianity, Canaanites were feared and hated. El is the ultimate god, and Baal and Anath are son and daughter, respectively. Mot is the lord of death and essentially eats Baal, and after 7 years Anath is able to set him free. The main part of this that was ushered into Christianity is the lord of death. Anath and Baal were gods but neither was totally evil, they balanced each other out.

Greece: we have hades and an underworld, although this underworld is not seen as a giant lake of fire, but fields of poplar trees. However, in some Jewish texts, Hades is referred to as Sheol, which was essentially a waiting place for souls before judgement. So this has made its way into the holy books. But here's the most influential part: Hermes has a son named Pan, who is the God of sexual desire. When Augustine became influential and sex began to be condemned, pan was the essential scapegoat-no pun intended. Pan has horns, goat legs and hooves, and is rather hairy. So if we return to the original paintings of the devil, he has horns, cloven feet, is red, and often hairy.

In Zoroastrianism, Ahura is the god of light and Ahriman is the force for war. Ahriman was the evil one. He was the force to rival the good god, also often depicted as a serpent, and was served by seven archfiends. Akin to the seven deadly sins in Christianity.

This ended up being much longer than anticipated but I hope it is informational!

Source: I'm literally reading a book called "The Devil: a Biography" by Peter Stanford right now, and when I saw this post I geeked out a little bit. You should check the book out if you're really interested!

To a certain extent, the lore (rather than the imagery) appears to come from a non-Biblical book called I Enoch which was written in about 300BC. This introduced ideas such as the fallen angels, which appear in later works such as the Divine Comedy. These ideas do not appear in the Bible - in fact there is very little in the Bible which connects with the Dantean vision. However there are clear references to it in the epistles Jude, I Peter and II Peter in the NT.

Although it appears that the ideas of I Enoch influenced ideas about hell and devils in mediaeval Christianity, it's difficult to know the detail. At least part of it was known to the Essenes, but their influence on early Christianity is debated. I Enoch was lost in the West until 1773, and as far as I know, it is not documented how it affected early Christianity.