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 ψ, and a scalar field φ, giving mass to ψ. The vector-like pair is defined 'exotic' because of a peculiar mass term of the color-triplet scalars, violating Baryon number as ∆B = 1. Such a mass term could be generated by exotic instantons in a class of string-inspired completions of the Standard Model: open (un-)oriented strings attached between D-brane stacks and Euclidean D-branes. A Post-Sphaleron Baryogenesis is realized through φ-decays into six quarks (antiquarks), or through ψ-decays into three quarks (antiquarks). This model suggests some intriguing B-violating signatures, testable in the next future, in NeutronAntineutron physics and LHC. We also discuss limits from FCNC. Sterile fermion can also be light as 1 − 100 GeV. In this case, the sterile fermion could be (meta)-stable and n −n oscillation can be indirectly generated by two n − ψ, ψ −n oscillations, without needing of an effective Majorana mass for neutron. Majorana fermion ψ can be a good candidate for WIMP-like dark matter.