Summary: In this paper, we define the notion of regular prime monomorphism for \(S\)-posets over a pomonoid \(S\) and investigate some categorical properties including products, coproducts and pullbacks. We study \(\mathcal{M}\)-injectivity in the category of \(S\)-posets where \(\mathcal{M}\) is the class of regular prime monomorphisms and show that the Skornjakov criterion fails for the regular prime injectivity. Considering a weaker form of such kind of injectivity, we obtain some classifications for pomonoids.