  We propose a generalization of the Grover-Sheng-Vishwanath model which, as
solved by the density-matrix renormalization group, realizes the emergent
supersymmetric criticality in the universality class of the even series of the
$\mathcal{N}\!=\!1$ superconformal minimal models characterized by a central
charge $5/4$. This chain model describes the topological phase transition of
the propagating Majorana edge mode in topological superconductors coupled with
the two-flavour Ising magnetic fluctuations (or the $XZ$ type). Using
bosonization and perturbative renormalization group, we show that the augmented
degrees of freedom trigger a paradigm shift from the supersymmetric
Landau-Ginzburg action to the variant of the supersymmetric sine-Gordon
equation, which, in the massless case, can flow towards the supersymmetric
minimal series upon a generalized Feigin-Fuchs construction. Therefore, the
present lattice model comprises a concrete system that exhibits the spacetime
supersymmetry through the distinct route.
