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The effects of the isovector-scalar $δ$-meson field on the properties of finite nuclei, infinite nuclear matter and neutron stars are investigated within the Relativistic Mean Field (RMF) model which includes non-linear couplings. Several parameter sets (SRV's) are generated to asses the influence of $δ$-meson on the properties of neutron star. These parametrizations correspond to different values of coupling constant of $δ$-meson to the nucleons with remaining ones calibrated to yield finite nuclei and infinite nuclear matter properties consistent with the available experimental data. It is observed that to fit the properties of finite nuclei and infinite nuclear matter, a stronger coupling between isovector-vector $ρ$ meson and nucleons is required in the presence of $δ$ field. Furthermore, the $δ$-meson is found to affect the radius of canonical neutron star significantly. The value of dimensionless tidal deformability, $Λ$ for the canonical neutron star also satisfies the constraints from the waveform models analysis of GW170817 binary neutron star merger event. A covariance analysis is performed to estimate the statistical uncertainties of the model parameters as well as correlations among the model parameters and different observables of interest.