  We consider two theoretical scenarios, each including a $\mathbb{Z}_{2}$-odd
sector and leading to an elementary dark matter candidate. The first one is a
variant of the Type-III seesaw model where one lepton triplet is
$\mathbb{Z}_{2}$-odd, together with a heavy sterile neutrino. It leads to a
fermionic dark matter, together with the charged component of the triplet being
a quasi-stable particle which decays only via a higher-dimensional operator
suppressed by a high scale. The second model consists of an inert scalar
doublet together with a $\mathbb{Z}_{2}$-odd right-handed Majorana neutrino
dark matter. A tiny Yukawa coupling delays the decay of the charged component
of the inert doublet into the dark matter candidate, making the former
long-lived on the scale of collider detectors. The parameter space of each
model has been constrained by big-bang nucleosynthesis constraints, and also by
estimating the contribution to the relic density through freeze-out of the
long-lived charged particle as well the freeze-in production of the dark matter
candidate. We consider two kinds of signals at the Large Hadron Collider for
the first kind of models, namely two charged tracks and single track + MET. For
the second kind, the characteristic signals are opposite as well as same-sign
charged track pairs. We perform a detailed analysis using event selection
criteria consistent with the current experimental programmes. It is found that
the scenario with a lepton triplet can be probed upto 960(1190) GeV with an
integrated luminosity of 300(3000) $fb^{-1}$, while the corresponding numbers
for the inert doublet scenario are 630(800) GeV. Furthermore, the second kind
of signal mentioned in each case allows us to differentiate different dark
matter scenarios from each other.
