Kill mudcrabs ..they are everywhere and plentiful. That will get you leather bits.
My main problem is creating medium armour. I can find plenty of jute but getting limited leather from beasts.
Seriously though, I've learned to level up with my Jute, because I never see anyone else picking it up. Then I save the leather for when I want to craft armor for myself or someone else.
There are a bunch of places that will provide rawhide scraps. Obviously I don't know what Alliance you're in, but in particular just outside Daggerfall is the Baelborn rock, full of imps. You can run a quick circuit there and get rawhide.