  Superconductivity in van der Waals materials, such as NbSe$_{2}$ and
TaS$_{2}$, is fundamentally novel due to the effects of dimensionality, crystal
symmetries, and strong spin-orbit coupling. In this work we perform tunnel
spectroscopy on NbSe$_{2}$ by utilizing MoS$_{2}$ or hexagonal Boron Nitride
(hBN) as a tunnel barrier. We observe subgap excitations and probe their origin
by studying various heterostructure designs. We show that the edge of
NbSe$_{2}$ hosts many defect states, which strongly couple to the
superconductor and form Andreev bound states. Furthermore, by isolating the
NbSe$_{2}$ edge we show that the subgap states are ubiquitous in MoS$_{2}$
tunnel barriers, but absent in hBN tunnel barriers, suggesting defects in
MoS$_{2}$ as their origin. Their magnetic nature reveals a singlet or a doublet
type ground state and based on nearly vanishing g-factors or avoided-crossing
of subgap excitations we highlight the role of strong spin-orbit coupling.
