I play a khajiit and for roleplay reason I want to only use claws.I've downloaded some mods to help,but how can I get the maximum vanilla damage for them?(The mod adds the perk for heavy armor which allows gloves to increase damage,so I can use that)I know there are enchantments that do increase the damage,but I can't find them,help please!

You want to find the pugilist's gloves for the enchantment, only item iirc with it.

You encounter the npc using them during a quest for the thieves guild

Other than that, there are no ways in vanilla to boost unarmed damage

besides the perk in heavy armor, that applys the base armor of heavy gloves to your fist damage

Do I have to do the entire thieves guild quest?I don't like the thieves guild.

not sure if you have to do any of the quests, the npc is in the ratway... not sure if they spawn before you're sent there though

Robbaz has a full guide on how to become an Unarmed badarse on YouTube Harry.

Disenchant the Gloves of the Pugilist, and put the enchantment on your heavy armour and jewellery. Take the Fists of Steel perk in the heavy armour tree.

And, as far as mods go... while it's probably extreme, Skyrim Redone (In addition to a bunch of other things) makes Khajiit unarmed claw damage one of the most powerful weapons in the game, and Unarmed combat gets a perk tree in Light Weapons.

I use light armor.But I do have a mod that gives the fist of steel perk to light armor too. PC ftw!

Nope, walk through the Ratways until you come across a guy who tries to beat you down (Gian the Fist)...he's wearing the Gloves of the Pugilist which is what you seek.

It sounds like you're ready to go and kick some ass.

Btw. You don't even need to as much as join the TG in order to get the Gloves. You can gain access to the Ratway without starting the questline.