Kinsue was also known as Kanin Daijin (Minister), since he inherited and lived in Kanin-dono (Kanin Palace), the former residence of FUJIWARA no Futsugu, and so Kinsue's descendants were said to belong to the Kanin-ryu.
藤原冬嗣の邸宅だった閑院殿を公季が伝領し住んだことから、閑院大臣の別称があり、その子孫は閑院流と呼ばれる。