All the neutrino/antineutrino experiments being performed in the few GeV energy region are using moderate to heavy nuclear targets where the contribution to the cross section comes from the quasielastic, inelastic and deep inelastic scattering processes. A better understanding of hadron dynamics in the nuclear medium is required to reduce the systematics considerably in the analyses of neutrino oscillation experiments. Presently 25-30% uncertainty in the systematics arises due to the lack of understanding of neutrino/antineutrino-A cross sections. Several theoretical as well as experimental efforts have been made to study the nuclear medium effects in the quasielastic and one pion production processes but the other inelastic and deep inelastic processes are not much explored. Recently we have performed a theoretical study of understanding nuclear medium effects in the DIS region for xA <=1 as well as for xA>1(Phys. Rev. D 105 (2022)033010, Phys. Rev. D 102 (2020)113007, arXiv:2202.11892[hep-ph]), using different nuclear targets such as hydrocarbon, argon and lead in the charged current vμ-A and ντ-A scattering processes. These results would be useful for the ongoing MINERvA's experimental analyses and also for the future accelerator and atmospheric neutrino experiments. In the numerical calculations, the nuclear medium effects like Fermi motion, binding energy and nucleon correlations are incorporated through the spectral function using a microscopic field theoretical model. The nucleon spectral function for an interacting Fermi sea is calculated using the nuclear many body theory and local density approximation has been used to obtain the results for a finite nucleus. Moreover, the coherent effects such as shadowing (x< 0.1) and antishadowing (0.1< x< 0.2) corrections as well as the mesonic cloud contributions (x< 0.6) have also been taken into account. While performing the numerical calculations for the evaluation of scattering cross sections, the target mass corrections (TMC) is incorporated and parton densities are evolved at the next-to-next-to-leading order (NNLO). This is the first theoretical calculation where a comparison of vμ-A and ντ-A DIS cross sections with nuclear medium effects has been made.