We have done a systematic no-core shell-model study of \(^{20-23}\) Na isotopes. The low-energy spectra of these sodium isotopes consisting of natural and un-natural parity states were reported, considering three realistic interactions: inside nonlocal outside Yukawa (INOY), charge-dependent Bonn 2000 (CDB2K), and the chiral next-to-next-to-next-to-leading order (N \(^3\) LO). We also present the mirror energy differences in the low-energy spectra of \(|T_z|\) = 1/2 mirror pair ( \(^{21}\) Na - \(^{21}\) Ne). Apart from the energy spectra, we have also reported the electromagnetic transition strengths and moments. Finally, considering all three realistic interactions, we report the point-proton radii and neutron skin thicknesses.