What should I use as a home remedy

Please take him to a vet.

Is he neutered? If not, he's going to get into more fights and get torn up.

What WonderGirl says.

Also, the results of his fights are probably going to keep getting worse. The first good abscess he gets will not respond well, if at all, to home treatment or remedies. And if he survives all the fighting, some sort of serious, if not fatal, disease is out there waiting for him.

Neutering him, even if he continues to spend his free time outdoors, will be the best money you can spend on his health. He will still get into an occasional fight, but not over a female.

You really should take him to a vet, and get him fixed (if he's not already).

If that really is not an option, then you need to clean the cuts with soap and water. Treat them the same way you would a cut on yourself, except using any topical antibiotic. Just make sure the cuts are clean, and check on them frequently. Don't use anything on the cuts that kitty could lick off.