We have investigated the existence of any possible pair breaking mechanism in Cu0.5Tl0.5Ba2Ca2Cu0.35Zn2.65O10−δ superconductor by carrying out post-annealing experiments in nitrogen, oxygen and air atmospheres. This material is grown in tetragonal structure with a and c-axes lengths 3.879 Å and 14.581 Å; the c-axis length is found to decrease with the increased concentration of Zn in the final compound. The substitution of Zn at CuO2 planar sites in formula unit Cu0.5Tl0.5Ba2Ca2Cu3−y Zny O10−δ has given superconductivity for all the Zn doping concentration of y = 0.75, 1.5, 2.25, 2.5, 2.65. The zero resistivity critical temperature [T c (R = 0)], the quantity of diamagnetism and critical current [I c (H = 0)]are found to increase with increased Zn doping. In Zn doped samples, post-annealing in air has given a maximum increase in superconducting properties, which showed that final material is optimally doped with carriers in ZnO2 planes. Since the superconducting properties are marginally suppressed in Zn doped samples by post annealing in O2 and N2 atmospheres, it has lead to a definite conclusion that pair breaking mechanism, suggested in previous studies, are absent altogether in our Cu0.5Tl0.5Ba2Ca2Cu0.35Zn2.65O10−δ superconductor. The synthesis of Cu0.5Tl0.5Ba2Ca2Zn3O10−δ superconductor by this method is extremely reproducible.