Utilizing the conformal-flatness nature of three-dimensional Anti-de Sitter (AdS 3) black hole solution of Banados, Teitelboim and Zanelli, the quantization of conformally-coupled scalar and spinor fields in this background space-time is explicitly carried out. In particular, mode expansion forms and propagators of the fields are obtained in closed forms. The vacuum in this conformally-coupled field theories in AdS 3 black hole space-time, which is conformally-flat, is the conformal vacuum which is unique and has global meaning. This point particularly suggests that now the particle production by AdS 3 black hole space-time should be absent. General argument establishing the absence of real particle creation by AdS 3 black hole space-time for this case of conformal triviality is provided. Then next, using the explicit mode expansion forms for conformally-coupled scalar and spinor fields, the bosonic and fermionic superradiances are examined and found to be absent confirming the expectation.