The Ashikaga shogun family is a line from Seiwa-Genji (Kawachi-Genji [Minamoto clan]) whose descendant demoted from nobility to subject so the family was an Imperial descendant (posterity) and was remotely related to the Imperial Family.
なお足利将軍家は、清和天皇の子孫が臣籍降下した清和源氏の一流（河内源氏）であり、皇胤であるため天皇家とは遠い血縁関係にあたる。