Most articles about state militia focus on antebellum companies in existence when the war began. The term 'Home Guard' usually implies state militia organized during the war. Little has been written about them.
Anyone with a serious interest in this topic should start at the state archives. The state constitution in effect during the war years will specify who was liable for militia service and what duties were expected of militiamen. The archives should contain rolls submitted from parishes where the militia organized (those not occupied by Federal troops). It would be worth checking the governor's papers and records of the state adjutant general.
For the most part, militia companies were expected to take up the duties of local law enforcement. In most states they enforced laws requiring men to enroll in the Confederate military. To that end home guards could visit homes and stop individuals to ask for passes, furlough papers and discharges. Failure to present proper papers usually resulted in arrest and punishment, sometimes on the spot.
You may also check state pension laws to see who was eligible. It's quite likely that Home Guards and others strictly in state service were ineligible to receive benefits. Of course Home Guards could still apply, and applications that the pension board denied may include much valuable information about state militia.