  The neutrino minimal Standard Model ({\nu}MSM) is the minimum extension of
the standard model. In this model, the Dodelson-Widrow mechanism (DW) produces
keV sterile neutrino dark matter (DM) and the degenerate GeV heavy Majorana
neutrinos lead to leptogenesis. However, the DW mechanism has been ruled out by
Lyman-{\alpha} bounds and X-ray constraints. An alternative scenario that
evades these constraints has been proposed, where the sterile neutrino DM is
generated by the thermal freeze-in mechanism via a singlet scalar. In this
paper, we consider a Higgs sector extension of the {\nu}MSM to improve dark
matter sectors and leptogenesis scenarios, focusing on the thermal freeze-in
production mechanism. We discuss various thermal freeze-in scenarios for the
production of keV-MeV sterile neutrino DM with a singlet scalar, and
reinvestigate the Lyman-{\alpha} bounds and the X-ray constraints on the
parameter regions. Furthermore, we propose thermal freeze-in leptogenesis
scenarios in the extended {\nu}MSM. The singlet scalar needs to be TeV scale in
order to generate the observed DM relic density and baryon number density with
the thermal freeze-in production mechanism.
