What relation is your son to your quarter cousin?

Answer 1

There is no relationship of "quarter cousin." If you have a first cousin, your son and that first cousin are first cousins, once removed. If you have a second cousin, your son and the second cousin are second cousins, once removed. Whatever cousin you have, your son and that cousin are the same kind of cousins, once removed.

Answer 2

Assuming your family isn't tangled up in some weird incestuous way, and that all the relations mentioned are "blood" ones and not "by marriage" or half-whatever or step-whatever, they would be second cousins.