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The present study investigates the isospin and Z-dependency of the effective symmetry energy and its coefficient , namely, neutron pressure for the isotonic chain of neutron magic N = 40, and 82. The relativistic mean-field model with the non-linear NL3 * parameter and Relativistic-Hartree-Bogoliubov approach with density-dependent DD-ME2 parameter sets are used for the analysis. The coherent density fluctuation model and Liquid-Drop-Approximation are adopted to formulate the nuclear matter observables such as symmetry energy, neutron pressure of finite nuclei at local density. We found a notable sign of the shell/sub-shell closure following the proton magic over the isotonic chain. Further, a comparative analysis shows that the coherent density fluctuation model is a better approximation to include the surface effect of finite nuclei as compared to the Liquid-Drop-Approximation, which plays a significant role to determine the shell/sub-shell closure over an isotopic and/or isotonic chain.