  We develop BRST symmetry for the first time for a particle on the surface of
a torus knot by analyzing the constraints of the system. The theory contains
$2^{nd}$ class constraints and has been extended by introducing Wess-Zumino
term to the convert it into a theory with first class constraints. BFV analysis
of the extended theory is performed to construct BRST/anti-BRST symmetries for
the particle on torus knot. The nilpotent BRST/anti-BRST charges which generate
such symmetries are constructed explicitly. The states annihilated by these
nilpotent charges consist the physical Hilbert space. We indicate how various
effective theories on the surface of the torus knot are related through the
generalized version of BRST transformation with finite field dependent
parameters.
