  We propose a minimal extension of Standard Model, generating a Majorana mass
for neutron, connected with a mechanism of Post-Sphaleron Baryogenesis. We
consider an `exotic vector-like pair' of color-triplet scalars, an extra
Majorana fermion $\psi$, and a scalar field $\phi$, giving mass to $\psi$. The
vector-like pair is defined `exotic' because of a peculiar mass term of the
color-triplet scalars, violating Baryon number as $\Delta B=1$. A
Post-Sphaleron Baryogenesis is realized through $\phi$-decays into six quarks
(antiquarks), or through $\psi$-decays into three quarks (antiquarks). This
model suggests some intriguing B-violating signatures, testable in the next
future, in Neutron-Antineutron physics and LHC. We also discuss limits from
FCNC.
  Sterile fermion can also be light as $1-100\, \rm GeV$. In this case, the
sterile fermion could be (meta)-stable and $n-\bar{n}$ oscillation can be
indirectly generated by two $n-\psi$, $\psi-\bar{n}$ oscillations, without
needing of an effective Majorana mass for neutron. Majorana fermion $\psi$ can
be a good candidate for WIMP-like dark matter.
