  We investigate a minimal neutrino portal dark matter (DM) model where a
right-handed neutrino both generates the observed neutrino masses and mediates
between the SM and the dark sector, which consists of a fermion and a boson. In
contrast to earlier work, we explore regions of the parameter space where DM is
produced via freeze-in instead of freeze-out motivated by the small neutrino
Yukawa couplings in case of $\mathcal{O} \left( \mathrm{TeV} \right)$ heavy
neutrinos. \\ For a non-resonant production of DM, its energy density is
independent of the DM mass. Assuming a democratic coupling structure we find
$M_N \approx 10 \, \mathrm{TeV}$. For the resonant production of DM, we find
that it can be produced via freeze-in or freeze-out even with couplings of
$\mathcal{O} \left( 10^{-5} \right)$. However, the measurement of the
Lyman-$\alpha$ forest rules out the feeble coupled freeze-out case completely,
while the resonant freeze-in production is only viable for $m_{DM} \gtrsim 3 \,
\mathring{keV}$.
