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Using Faddeev-Senjanovic path integral quantization for constrained Hamiltonsystem, we quantize SU(n) N=2 supersymmetric gauge field system withnon-abelian Chern-Simons topological term in 2+1 dimensions, and useconsistency of a gauge condition naturally to deduce another gauge condition.Further, we get the generating functional of Green function in phase space,deduce the angular momentum based on the global canonical Noether theorem atquantum level, obtain the fractional spin of this supersymmetric system, andshow that the total angular momentum has the orbital angular momentum and spinangular momentum of the non-abelian gauge field. Finally, we find out theanomalous fractional spin and discover that the fractional spin has thecontributions of both the group superscript components and the A_0^s (x)charge.

Faddeev-Senjanovic Quantization of SU(n) N=2 Supersymmetric Gauge Field System with Non-Abelian Chern-Simons Topological Term and Its Fractional Spin