  We examine the Scotogenic model employing the TM$_2$ mixing matrix,
$U_{\text{TM}_2}$, for neutrinos and parameterize the Yukawa coupling matrix
$y$ based on the diagonalization condition for the neutrino mass matrix,
$m_{\nu}$. Our investigation centers on analyzing the relic density of cold
dark matter ($\Omega h^2$) and possible lepton flavor violation (LFV) in the
model. In particular, we study coannihilation dynamics and LFV, in the model,
considering various coannihilation scenarios including non-zero mass splitting
between lightest sterile neutrinos. While analyzing, we have taken into
consideration respective experimental constraints on $\Omega h^2$ and LFV
alongside neutrino oscillation data. Our study reveals that in both normal and
inverted hierarchy of neutrino masses, splitting between masses of $N_1$ and
$N_2$ can be up to $\approx 15\%$ for the model to be in consonance with the
above constraints. In the second part, we have extended the analysis
incorporating extended magic symmetry in $m_\nu$ enabling us to completely
determine Yukawa coupling matrix ($y$). We observe a notable exclusion of the
effective Majorana mass $|m_{ee}|$ parameter space by cosmological bound on sum
of neutrino masses, particularly in the normal hierarchy while inverted
hierarchy scenario is excluded due to constraints coming from extended magic
symmetry. These findings shed light on the interplay among the Scotogenic
model, TM$_2$ mixing, and extended magic symmetry, offering insights into the
permitted parameter space and hierarchy exclusion.
