Melody,Many years ago we lived in Tennessee and we visited the Cherokee Nation and a museum I believe was there. One of the men I worked with was named Poteat and was part Cherokee. I didn't know there were Cherokees named Fugate.
Since Fugate is an English derivation of a French name (we think) it would appear that sometime in the 1800's, a Fugate man married a Cherokee woman and the name has come down to the present day.I don't know if there are any Cherokee records that would record this.Would be nice if there were records.
You are fortunate that one of your traceable ancestors is named Seaberry as this is an unusual name and appears is several census records.
The Fugates that we all descend from, arrived in Maryland around 1650 near present day Annapolis and one record lists Mosquito Creek.A couple of names are mentioned in the many records of those Fugates - Peter and James. We believe they are French for various reasons, but do have records that indicate they stopped first in England.They might have been Huguenots (French Protestants) who were run out of France.
From there the Fugates expanded westward into Virginia and from there into Kentucky, North Carolina, Tennessee and other states.The North Carolina Fugates would have come from those early Maryland Fugates. I haven't researched the Wilkes County, NC Fugates, so I don't have much information at the present time.But there might be some record that would indicate who Martha Frankie Fugate's parents were.You must have quite a bit of information from Robert Arms and Martha down to your present day relatives.