I am reading a paper on Hobbes interpretation of patriarchy, which says hobbes patriarchy is non paternal, i.e. he proposes a patriarchal right that is different from paternal right? What is the exact difference between the two?
Well, it sounds like you are reading a paper on exactly this topic, so I imagine you already have the answer ready-to-hand.
In any event, for Hobbes, nature (or natural law) endows the Mother with authority over the family, and he argues that it is a social contract that shifts this authority to the Father as "sovereign".
Thus, for him, patriarchy is contingent upon human decisions, and is not properly a paternal right (i.e., natural to the father.) This puts him at odds with other supporters of patriarchy who argue precisely this.