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In this study, we calculate the nuclear matrix elements (NMEs) for the lightneutrino-exchange mechanism of neutrinoless double beta $0\nu\beta\beta$) decayof $^{124}$Sn within the framework of the interacting nuclear shell model usingthe effective shell model Hamiltonian GCN5082. A novel method based on anonclosure approach is employed, wherein for the intermediate nucleus$^{124}$Sb, effects of energy of 100 states for each $J_{k}^{\pi}$=$0^{+}$ to$11^{+}$ and $2^{-}$ to $9^{-}$ ($\Delta J_{k}$=1) are explicitly included inthe NMEs calculation. Other common effects such as the finite size of nucleons,higher-order effects of nucleon currents, and short-range correlations (SRC) ofnucleons are also taken into account. The extracted optimal closure energy is2.9 MeV for a total NME of $^{124}$Sn $0\nu\beta\beta$ decay, which isindependent of different forms of SRC parametrizations. A comparison of NMEsand half-lives with some of the recent calculations is presented. Further, togain a comprehensive understanding of the role of nuclear structure on the$0\nu\beta\beta$ decay, the dependence of NMEs on spin-parity of theintermediate states, coupled spin-parity of neutrons and protons, and thenumber of intermediate states, is explored. It is observed that the inclusionof the effects of excitation energies of the intermediate nucleus yields morereliable NMEs. The present findings provide valuable insights for experimentalinvestigations of $0\nu\beta\beta$ decay of $^{124}$Sn in India and elsewhere.

Nuclear matrix elements calculation for $0\nu\beta\beta$ decay of $^{124}$Sn using nonclosure approach in nuclear shell model