  We study the effect of photonic spin-orbit coupling (SOC) in micropillar
lattices on the topological edge states of a one-dimensional chain with a
zigzag geometry, corresponding to the Su-Schrieffer-Heeger model equipped with
an additional internal degree of freedom. The system combines the strong
hopping anisotropy of the $p$-type pillar modes with the large TE-TM splitting
in Bragg microcavities. By resolving the photoluminescence emission in energy
and polarization we probe the effects of the resulting SOC on the spatial and
spectral properties of the edge modes. We find that the edge modes feature a
fine structure of states that penetrate by different amounts into the bulk of
the chain, depending on the strength of the SOC terms present, thereby opening
a route to manipulation of the topological states in the system.
