There are two red flags in your post. First, you claim your family to be "aristocrats." What does that mean? Have you fallen into the outdated genealogical trap that your ancestors can only be interesting if they are royals or Indians? And second, there was no "Cherokee Chief" named Beauregard Giga. Please don't confuse family oral history with fact. Genealogical research is a science and must be approached in a systematic and scientific way. Start with yourself and prove each generation as far back as you can go. Your work will be more credible and you won't be purpetuating false information about your family or the Cherokee people.