Before we get to the nitty gritty of this question - let us all agree on one thing here: YES they are in the Bible. The question is WHERE did they originate?
Many will come to this question ready to tell me that demons are fallen angels per Revelation 12:9, but that cannot be because this event cannot have happened unless you can explain retconning the rest of Revelation, as the following chapter reveals the Beasts. We also must understand that, as possibly the most important prophecy and one inspired by Christ himself, that this event would be chronological and in order as to not confuse the reader. The goal was for us to understand, not be confused. This is not (or it shouldn't) depend on a denomination, since we all know the Lord is not the author of confusion.
Bringing up Revelation 1:19, a lot of people seem to disregard Revelation 4:1, which tells us the events following are events to happen. Therefor, the War in Heaven has not happened yet because it takes place during the Tribulation, and if I'm not mistaken, just before Christ's millennial reign as far as how it's written.
Now to the question - is there a biblical basis for the origin of demons?
The fall of the angels in Genesis can't be, because all life was destroyed by the Flood (and if you consider Enoch canonical as some do, they are bound until judgement).
We see throughout Scripture that these demons are evil spirits in Matthew 10:1, unclean spirits in Mark 1:27, and lying spirits in 1 Kings 22:23
The closest inkling, if at all, to their origin is in Ephesians 6:12, where Paul writes:
For we do not wrestle against flesh and blood, but against the rulers, against the authorities, against the cosmic powers over this present darkness, against the spiritual forces of evil in the heavenly places.
I've tried to find some sort of origin for demons, but have found nothing. I ask because (I feel) it is somewhat necessary to understand, and therefor identify, this evil.