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The proposed work is an extension of the Standard Model, where we have introduced two gauge symmetries, i.e., $U(1)_{B-L}$ and $U(1)_{L_e-L_μ}$ to study neutrino phenomenology, muon, and electron $(g-2)$ as well as leptogenesis using the inverse seesaw mechanism. For this purpose, we have included three right-handed neutrinos $N_{R_i}$, three neutral fermions $S_{L_i} (i =1,2,3)$ and two scalar singlet bosons ($χ_1$ and $χ_2$). We get a definite structure for the neutrino mass matrix due to the aforementioned gauge symmetries. Thus, our model is able to predict the neutrino oscillation results, which are in accordance with the experimental data and is inclined towards normal ordering. The outcomes comprise the active neutrino masses, mixing angles, mass squared differences, CP-violating phase, etc. Moreover, since the extended gauge symmetries are local, there are corresponding gauge bosons, denoted as $Z_{B-L}$ and $Z_{e μ}$. Of these, mass of $Z_{B-L}$ is $\mathcal{O}$(TeV) range to satisfy the collider constraint, while the mass of $Z_{e μ}$ is in the MeV range, making it feasible to account for current electron and muon $(g-2)$ results via neutral current interactions. Furthermore, our model is able to account for leptogenesis, which can demonstrate the matter-antimatter asymmetry of the universe. Additionally, we have carried out the prospect of probing our model in the context of upcoming long baseline experiments: DUNE, T2HK, and T2HKK, at a confidence level of $5σ$. From the result it is clear that, our model can be tested in its $3σ$ C.L. with $5σ$ allowed region of DUNE, T2HK and T2HKK.