  We study the topological classification of parafermionic chains in the
presence of a modified time reversal symmetry that satisfies ${\cal T}^2=1 $.
Such chains can be realized in one dimensional structures embedded in
fractionalized two dimensional states of matter, e.g. at the edges of a
fractional quantum spin Hall system, where counter propagating modes may be
gapped either by back-scattering or by coupling to a superconductor. In the
absence of any additional symmetries, a chain of $\mathbb{Z}_m$ parafermions
can belong to one of several distinct phases. We find that when the modified
time reversal symmetry is imposed, the classification becomes richer. If $m $
is odd, each of the phases splits into two subclasses. We identify the symmetry
protected phase as a Haldane phase that carries a Kramers doublet at each end.
When $m $ is even, each phase splits into four subclasses. The origin of this
split is in the emergent Majorana fermions associated with even values of $m$.
We demonstrate the appearance of such emergent Majorana zero modes in a system
where the constituents particles are either fermions or bosons.
