  Strongly correlated systems exhibit a rich phenomenology due to the
antagonism of a diversity of ordered phases. The aftermath of this interplay
can lead to a coexistence which takes place at a microscopic level, or, a phase
separation in which non-overlapping single-order domains extend throughout the
material. In most cases it appears experimentally challenging to disentangle
the two scenarios, unless, there exist robust and measurable properties
particular to only one of the two types of coexistence. This is for instance
the case when the type of coexistence decides on the appearance of
topologically protected excitations, such as, Majorana fermions. In this work,
we explore a concrete example falling into this category of systems, and
specifically, we investigate one-dimensional odd-parity spin-triplet
superconductors in the presence of antiferromagnetism. We determine the
symmetry conditions for the occurrence of Majorana edge states and explore
their response to variations of the strength and orientation of the
antiferromagnetic field $\boldsymbol{M}$, as well as, the spin structure of the
Cooper pairs controlled by the so-called $\boldsymbol{d}$-vector.
