All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
It is permissible to swear by the Mercy of Allaah The Exalted but not by the mercy of any created being, because the mercy of any created being is created as well, and it is forbidden to swear by something that is created. Therefore, if you mean by, “I swear by your dead father's mercy,” to swear by the Mercy of Allaah The Exalted that He Bestowed on your dead father, this oath is permissible. However, if you mean to swear by your father's mercy, i.e. the mercy of a created being, then this oath is impermissible because you are swearing an oath by a created being.
Allaah Knows best.