  In this work, we present a comparative study of the three of the seesaw
models, viz., type II, inverse and linear seesaw models, to investigate about
light neutrino masses and mixings, flavour structure, neutrinoless double beta
decay ($ 0\nu \beta \beta $) and charged lepton flavour violation (cLFV) decay
($\mu\rightarrow e\gamma$). We consider the $ A_{4} $ flavour symmetry, while
some other symmetries, like $U(1)_{X}$, $Z_4$ and $Z_5$ are also included to
forbid unwanted terms in the Lagrangian. Taking into account the present
experimental data for the known light neutrino parameters from recent global
fit data, we compute the currently unknown neutrino parameters such as the
lightest neutrino mass ($m_1$), CPV phase (Dirac and Majorana), and effective
light neutrino mass in the neutrinoless double beta decay, by considering
different VEV alignments of the triplet scalar flavon fields. We also elucidate
on the octant of atmospheric neutrino mixing angle, $\theta_{23}$, in the light
of our predicted results. Finally, we present the region of parameter spaces of
$m_1$, CPV phases, octant of $\theta_{23}$ and effective mass measurable in of
neutrino less double beta decay experiments, that can be tested in future
experiments. We observe that the branching ratio of ($\mu\rightarrow e\gamma$)
can help discriminate the three seesaw models. Further, the favoured Octant of
the atmospheric mixing angle $\theta_{23}$ changes with the VEV alignment of
the triplet flavon field - i.e., the internal flavour structure of the
neutrinos is reflected in their composition (mixing). The constant F
determining the scale of flavour symmetry breaking, seesaw scale and coupling
constants of the three seesaw models has also been computed, which puts a
constraint among them allowed by the present experimental results.
