  \textbf{T}he \textbf{IN}dia's \textbf{TIN} (TIN.TIN) detector is under
development in the search for neutrinoless double-$\beta$ decay
(0$\nu\beta\beta$) using 90\% enriched $^{124}$Sn isotope as the target mass.
This detector will be housed in the upcoming underground facility of the
\textbf{I}ndia based \textbf{N}eutrino \textbf{O}bservatory. We present the
most important experimental parameters that would be used in the study of
required sensitivity for the TIN.TIN experiment to probe the neutrino mass
hierarchy. The sensitivity of the TIN.TIN detector in the presence of sole two
neutrino double-$\beta$ decay (2$\nu\beta\beta$) decay background is studied at
various energy resolutions. The most optimistic and pessimistic scenario to
probe the neutrino mass hierarchy at 3$\sigma$ sensitivity level and 90\% C.L.
is also discussed.
