Something handed down from an ancestor, a predecessor, or from the past is called
a. a story
b. a legacy
c. a root
d. a fallacy

It would be a root, since it is something that is continuously growing and has been in the family since ancient times. Just like a tree growing, in essense. A legacy is something left behind that is very important to the family but typically doesn't exist today, a story is obviously something that is told or spoken of, and a fallacy is a mistaken belief/unfound argument.