  While the $\mathbb{Z}_3$ symmetric dark matter models have shown tremendous
prospects in addressing a number of (astro-)particle physics problems, they can
leave interesting imprints on cosmological observations as well. We consider
two such promising models: semi-annihilating dark matter (SADM) and Co-SIMP
$2\rightarrow 3$ interaction, and investigate their effects on the global 21-cm
signal. SADM alone cannot address the EDGES dip but can perform better with the
aid of an excess radio background, whereas Co-SIMP can naturally explain the
EDGES absorption feature by virtue of an intrinsic cooling effect without
invoking any such excess radiation. Hence, the latter model turns out to be a
rare model within the domain of CDM, that uses leptophilic interaction to
achieve the EDGES dip. Further, keeping in mind the ongoing debate between
EDGES and SARAS 3 on the global 21-cm signal, we demonstrate that our chosen
models can still remain viable in this context, even if the EDGES data requires
reassessment in future. We then extend our investigation to possible
reflections on the Dark Ages, followed by a consistency check with the CMB and
BAO observations via Planck 2018(+BAO) datasets. This work thus presents a
compelling case of exploring these interesting particle physics models in the
light of different cosmological observations.
