Oh boy! Something I can help with! I'm doing an Honors Thesis on Loyalists (Specifically Scottish Highlanders) in North Carolina but I can definitely help!

Clark, Murtie June. Loyalists in the Southern Campaign of the Revolutionary War. Balitmore: Genealogical Publishing Co, 1981.

Demond, Robert O. Loyalists in North Carolina During the Revolution. Durham: Duke University Press, 1940.

Roster of Soldiers from North Carolina in the American Revolution. Published by The North Carolina Daughters of the American Revolution, 1932.

Clark's has a lot of the Southern Regiments of Loyalist militias, The Roster is mostly Patriot militias. These are the muster lists and I think some include what battle they fought at, who was absent due to sickness, payment they require, etc.

I hope your university library has it because those two are long out of print. However, Demond's book does include the Loyalist Militia lists for NC so that helps if you can't find the others.

Depending what you're looking at, I can help more with resources.