  In this study, we calculate the nuclear matrix elements (NMEs) for the light
neutrino-exchange mechanism of neutrinoless double beta $0\nu\beta\beta$) decay
of $^{124}$Sn within the framework of the interacting nuclear shell model using
the effective shell model Hamiltonian GCN5082. A novel method based on a
nonclosure 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 in
the NMEs calculation. Other common effects such as the finite size of nucleons,
higher-order effects of nucleon currents, and short-range correlations (SRC) of
nucleons are also taken into account. The extracted optimal closure energy is
2.9 MeV for a total NME of $^{124}$Sn $0\nu\beta\beta$ decay, which is
independent of different forms of SRC parametrizations. A comparison of NMEs
and half-lives with some of the recent calculations is presented. Further, to
gain a comprehensive understanding of the role of nuclear structure on the
$0\nu\beta\beta$ decay, the dependence of NMEs on spin-parity of the
intermediate states, coupled spin-parity of neutrons and protons, and the
number of intermediate states, is explored. It is observed that the inclusion
of the effects of excitation energies of the intermediate nucleus yields more
reliable NMEs. The present findings provide valuable insights for experimental
investigations of $0\nu\beta\beta$ decay of $^{124}$Sn in India and elsewhere.
