The web novels are usually subscription services.
The sites like Royal Road, or Scribble Hub, are used as an advertisement of sots, slowly posting the chapters, encouraging the impatient readers to pay for subscription via Patreon where they could the next chapter faster than it is normal, usually some ten or fifteen chapters in advance. Technically, it is not called subscription, but it is how it usually works. That's the usual business model.
You could, of course, monetise your own work in any way you feel is appropriate, but this is how it works for others, and what most people expect.
Either subscription for advanced chapters, or selling the complete books ahead of time.
Selling "fan-fiction" of your own work is technically legal. It's not even fan-fiction, it's adaptation, because, well, you own copyright for your own work (unless you sign it off to others), but the readers who support you on Patreon usually want the original story, not the variation of it. Asking for donation is fair game, but you will get very few takers. Unless your idea is very, very popular.
A term "fan-fiction" is also nebulous. You couldn't sell "fan-fiction" of the works you do not own, that's copyright violation, and you will be sued. Technically, you couldn't even write it for free, that's also copyright violation (but some sites might look away).