  We introduce a novel class of low-dimensional topological tight-binding
models that allow for bound states that are fractionally charged fermions and
exhibit non-Abelian braiding statistics. The proposed model consists of a
double (single) ladder of spinless (spinful) fermions in the presence of
magnetic fields. We study the system analytically in the continuum limit as
well as numerically in the tight-binding representation. We find a topological
phase transition with a topological gap that closes and reopens as a function
of system parameters and chemical potential. The topological phase is of the
type BDI and carries two degenerate mid-gap bound states that are localized at
opposite ends of the ladders. We show numerically that these bound states are
robust against a wide class of perturbations.
