Topological superconductors are an essential component for topologically protected quantum computation and information processing. Although signatures of topological superconductivity have been reported in heterostructures, material realizations of intrinsic topological superconductors are rather rare. Here we use scanning tunnelling spectroscopy to study the transition metal dichalcogenide 4Hb-TaS₂ that interleaves superconducting 1H-TaS₂ layers with strongly correlated 1T-TaS₂ layers, and find spectroscopic evidence for the existence of topological surface superconductivity. These include edge modes running along the 1H-layer terminations as well as under the 1T-layer terminations, where they separate between superconducting regions of distinct topological nature. We also observe signatures of zero-bias states in vortex cores. All the boundary modes exhibit crystallographic anisotropy, which—together with a finite in-gap density of states throughout the 1H layers—allude to the presence of a topological nodal-point superconducting state. Our theoretical modelling attributes this phenomenology to an inter-orbital pairing channel that necessitates the combination of surface mirror symmetry breaking and strong interactions. It, thus, suggests a topological superconducting state realized in a natural compound.