  We study the effect of strong spin-orbit coupling (SOC) on bound states
induced by impurities in superconductors. The presence of spin-orbit coupling
breaks the $\mathbb{SU}(2)$-spin symmetry and causes the superconducting order
parameter to have generically both singlet (s-wave) and triplet (p-wave)
components. We find that in the presence of SOC the spectrum of
Yu-Shiba-Rusinov (YSR) states is qualitatively different in s-wave and p-wave
superconductor, a fact that can be used to identify the superconducting pairing
symmetry of the host system. We also predict that in the presence of SOC the
spectrum of the impurity-induced bound states depends on the orientation of the
magnetic moment $\bf{S}$ of the impurity and, in particular, that by changing
the orientation of $\bf{S}$ the fermion-parity of the lowest energy bound state
can be tuned. We then study the case of a dimer of magnetic impurities and show
that in this case the YSR spectrum for a p-wave superconductor is qualitatively
very different from the one for an s-wave superconductor even in the limit of
vanishing SOC. Our predictions can be used to distinguish the symmetry of the
order parameter and have implications for the Majorana proposals based on
chains of magnetic atoms placed on the surface of superconductors with strong
spin-orbit coupling.
