Greeting you have a few good point to start from Your grand father Randolph see if you can locate his birth records that should pin point his parents then go on from there access cencus to see where they lived and the chance of finding siblings. collect birth,Marriage cetificates and death certiicates there are some time details of family members listed on thoes documents to prove you are on the right track and dates. hope that was of help.
Good luck
Jahrome