The quantization of charged matter system coupled to Chern-Simons gauge fields is analyzed in a covariant gauge fixing, and gauge invariant physical anyon operators satisfying fractional statistics are constructed in a symmetric phase, based on Dirac's recipe performed on QED. This method provides us a definite way of identifying physical spectrums free from gauge ambiguity and constructing physical anyon operators under a covariant gauge fixing. We then analyze the statistical spin phase

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... tion in a symmetry-broken phase and show that the Higgs mechanism transmutes an anyon satisfying fractional statistics into a canonical boson, a spin 0 Higgs boson or a topologically massive photon.