Was searching for fiction and this thread shows up... Anyway..

I used to frequent FanFiction.net (on mobile) to read fanfics. They have an app now, which is immensely improved. Stories may or may not be better as I haven't been back in ages.. Note that its app works a lot better than its desktop version now.

It has a sister site, FictionPress.net - this is where all stories published are not fanfics. Not sure if it has an app but its worth checking it out.

Try looking into wattpad and archive of our own too. Looks like they are publishing independent stories from independent authors (mostly budding authors lol).