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The current upper limit on $N_{\rm eff}$ at the time of CMB by Planck 2018can place stringent constraints in the parameter space of BSM paradigms wheretheir additional interactions may affect neutrino decoupling. Motivated by thisfact in this paper we explore the consequences of light gauge boson ($Z'$)emerging from local $U(1)_X$ symmetry in $N_{\rm eff}$ at the time of CMB.First, we analyze the generic $U(1)_X$ models with arbitrary charge assignmentsfor the SM fermions and show that, in the context of $N_{\rm eff}$ the generic$U(1)_X$ gauged models can be broadly classified into two categories, dependingon the charge assignments of first generation leptons. We then perform adetailed analysis with two specific $U(1)_X$ models: $U(1)_{B_3-3L_e}$ and$U(1)_{B_3-3L_\mu}$ and explore the contribution in $N_{\rm eff}$ due to thepresence of $Z'$ realized in those models. For comparison, we also showcase theconstraints from low energy experiments like: Borexino, Xenon 1T, neutrinotrident, etc. We show that in a specific parameter space, particularly in thelow mass region of $Z'$, the bound from $N_{\rm eff}$ (Planck 2018) is morestringent than the experimental constraints. Additionally, a part of theregions of the same parameter space may also relax the $H_0$ tension.

Hubble Tension and Cosmological Imprints of $U(1)_X$ Gauge Symmetry: $U(1)_{B_3-3 L_i}$ as a case study