In near-zero-permittivity operation range, the position-dependent extraordinary optical properties of a one dimensional (1D) Fibonacci quasi-periodic superconducting photonic crystal (PC), which consists of alternating superconductor and dielectric layers, are theoretically investigated by using the transfer matrix method. Based on the calculated reflectance spectrum, it is shown that the extraordinary optical properties depend on the relative positions of the threshold wavelength and the photonic band gaps (PBGs). By suitably choosing the thickness of the superconducting or dielectric layer, a transmission narrow band filter or resonator can be designed without introducing any physical defect in this structure.