You don't actually have to pay for copyright unless you specifically filed a patent which is... a different, more complicated thing involving turning stuff into trademarks and loopholes used to extend the copyright on characters like Mickey Mouse and Batman. On a simple level though, the moment you put your work on the internet, you own the copyright to that work.
Except... the copyright is only afforded you if you seem to care about it and could argue in court that you did try to protect your right as sole owner of characters and concepts from your series. This is where things get tricky. Let's use Photoshop as an example...
When you edit an image, you might use the verb "to photoshop", ie. "I photoshopped it" "That looks photoshopped." even if it was done in another program, like say GIMP or Clip Studio. Adobe hates this. See, the thing is, if a brand name gets "genericised", and people start using it as a general term for that thing, like how people in the US use "band-aid" for all adhesive wound dressings, or how here in the UK we use "hoovering" as a generic term for vaccuum cleaning, somebody could argue in court that that's now a generic term and so that they have the right to name their product "The Super Hoover" without it being of Hoover brand, or "Photoshop Deluxe" without it being anything to do with Adobe Photoshop. For this reason, Adobe says on a page of their site:
You must never use the Photoshop trademark as a common verb ('to photoshop an image,” as an example of such incorrect use) or as a noun.
The same thing can happen to stories, and it's less specifically the entire story or franchise itself, and more just bits and bobs, like concepts, characters etc. For example, Mithril, the mystical metal from Lord of the Rings, has become genericised and turns up in all sorts of Fantasy games and stories, though it was invented by Tolkien, and now the Tolkien estate is super-protective of any names that haven't, like Rohirrim.
Companies actually put a ton of work into defining what the "distinctive features" of their characters are specifically for the purposes of defining what is their character and what is "legally distinct" from them. For example, I worked on a Doctor Who book, and painted the Tardis a sort of Indigo blue colour, and the BBC were like "it needs to be this shade of blue", because if it's not on-brand, and they're not seen as making efforts to preserve the brand identity, they could lose copyright of the Tardis, an object that they already had to have a legal dispute over with the British Police, because of course, it looks like an old Police box. The BBC lawyers argued that in the eyes of most people, since police boxes haven't been a thing on the streets since like the 70s and the police have made no effort to protect the copyright of the police box, that it is more recognisable as a Tardis now and the Tardis' appearance should be copyright to them... and they won!
So actually, YES. If your Disney fan comic got super-popular, and people started associating a character or concept more strongly with your fancomic than the original Disney thing they were in, Disney COULD actually lose the copyright! It's unlikely to happen with Mickey Mouse, but it's not out of the question if you dug up some more obscure characters and they became more associated with your work than Disney's and Disney didn't make a visible effort to tell you to stop; that would be seen as a sign of them accepting it and basically giving up and letting you take it. And that's why Disney, Nintendo and similar come down so hard on fan stuff, because they're companies that rely most heavily on their characters and established franchises.
And that's why you need to be careful about fan works.