  An unusual form of superconductivity, called Ising superconductivity, has
recently been uncovered in mono- and few-layered transition metal
dichalcogenides. This 2D superconducting state is characterized by the
so-called Ising spin-orbit coupling (SOC), which produces strong oppositely
oriented effective Zeeman fields perpendicular to the 2D layer in opposite
momentum space valleys. We examine the Yu-Shiba-Rusinov (YSR) bound states
localized at magnetic impurities in Ising superconductors and show that the
unusual SOC manifests itself in unusually strong anisotropy in magnetic field
response of zero bias conductance peaks observable in STM experiments on
impurity sites. For a chain of magnetic impurities with moments parallel to the
plane of Ising superconductors we show that the low energy YSR band can host
topological superconductivity and Majorana fermions as a direct manifestation
of Ising spin-orbit coupling induced topological effects.
