Fast charging only works up to 50%, then it reverts to normal charging. The problem is that you should never let the battery drop to less than 40%, so fast charging doesn't do much.
If you've constantly allowed the battery to drop to 10% (or less), it's probably about shot, and you need a new battery. And this time, either charge it when it drops to 40%, carry a power pack with you and connect it when the battery drops to 40% or turn the phone off if you can't do either one when the battery drops to 40%.
It's not Samsung's fault, it's not the battery's fault, lithium batteries are not deep discharge batteries. If they used lead acid batteries, we could discharge them to 0% all the time for years, but a lead acid battery with enough capacity to power a phone would weigh a few pounds. (And you'd be carrying a little tub of sulfuric acid in your pocket, which you wouldn't want to do. One crack and your pocket - and your leg - would get burned.)