Effects of a superstrate layer on the resonant frequency and bandwidth of a high Tc superconducting (HTS) circular printed patch are investigated in this paper. For that, a rigorous full-wave spectral analysis of superconducting patch in multilayer configuration is described. In such an approach, the spectral dyadic Green's function which relates the tangential electric field and currents at various conductor planes should be determined. Integral equations are solved by a Galerkin's moment method procedure, and the complex resonance frequencies are studied with basis functions involving Chebyshev polynomials in conjunction with the complex resistive boundary condition. To include the superconductivity of the disc, its complex surface impedance is determined by using London's equation and the model of Gorter and Casimir. Numerical results are compared with experimental results of literature as well as with the most recent published calculations using different methods. A very good agreement is obtained. Finally, superstrate loading effects are presented and discussed showing interesting enhancement on the resonant characteristics of the superconducting antenna using combinations of Chebyshev polynomials as set of basis functions.