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About 12 to 15 years ago I read a book that started off as a sword and sorcery-style book about a land surrounded by a thick fog wall. I don't remember who wrote it or what it was called. If I remember right, people who were exiled were sent through the fog, never to be heard from again. Towards the end of the book, the hero was banished through the fog. On the other side, he found a sci-fi sort of setting with armies trying to find a way to penetrate the fog wall.

I'm pretty sure this was a trilogy. I want to say it was published by Tor, but I can no longer trust my memory on these things. I think the main hero had a sword or was born with an ability that made him immune to magic (or unable to cast it).

This sounds like Jack Chalker's Soul Rider series. https://www.goodreads.com/series/41590-soul-rider

The lands are called "anchors", and the fog is called "flux". People with control of flux appear to do magic, but are actually able to communicate with the computers that shape the flux.

In the first book written, a young girl is exiled/sold into slavery in flux. Unknown to anyone, the computers have set a high-tech monitoring device on her (a Soul Rider), which is how they keep tabs on the world. The presence of the Soul Rider limited what the computers would permit to be done to her in flux, so she was largely immune to "magic".

Through the series, you learn that the state of the world is due to an aborted teraforming. The original plan was to cover the world in flux, which could be worked through computers. The Anchors were lands built to house the computers. The next step was to build the lands between the anchors, but something went wrong at this point (no spoilers!) and the project was aborted.

There's a very good chance that this is the Darksword trilogy. The first book was originally published January 1988. The protagonist Joram is born "dead", unable to wield magic. He wields the titular Darksword, which is itself immune to magic. He may also have a Darkstone amulet, that protects him from magic. In the second book, he and Gwendolyn are banished. Later it is revealed that the world outside has technology, possibly in the third book Triumph of the Darksword.
Later the more modern day armies attempt to invade. I believe Joram unites his people to resist the invasion. Apologies for the vagueness, it's been decades since I've read the series.