The fundamental group of a knot complement is called a knot group. A way to present a knot groups is the Wirtinger presentation, which is given by a conjugation action at each crossing of the knot. This presentation is also given by a conjugate quandle, which matches well to the Hopf algebra structure of the group ring of the knot group. Here we introduce the braided conjugate quandle corresponding to the braided Hopf algebra, which is a deformation of a Hopf algebra. A typical example of the braided Hopf algebra is the braided SL(2) introduced by S. Majid, and so it may give a q-deformation of a SL(2) representation of the knot group. This is joint with Roland van der Veen.