  Superconducting topological systems formed by a strong 3D topological
insulator (TI) in proximity to a conventional $s$-wave superconductor (SC) have
been intensely studied as they may host Majorana zero modes. However, there are
limited experimental realizations of TI-SC systems in which robust
superconducting pairing is induced on the surface states of the TI and a
topological superconducting state is established. Here, we fabricate a novel
TI-SC system by depositing, via focused ion beam, tungsten (W) nanoscale
clusters on the surface of TI Bi$_{0.91}$Sb$_{0.09}$. We find that the
resulting heterostructure supports phase-slip lines that act as effective
Josephson junctions. We probe the response of the system to microwave
radiation. We find that for some ac frequencies, and powers, the resulting
Shapiro steps' structure of the voltage-current characteristic exhibits a
missing first step and an unexpectedly wide second Shapiro step. The
theoretical analysis of the measurements shows that the unusual Shapiro
response arises from the interplay between a static Josephson junction and a
dynamic one, and allows us to identify the conditions under which the missing
first step can be attributed to the topological nature of the Josephson
junctions formed by the phase-slip lines. Our results suggest a new approach to
induce superconductivity in a TI, a novel route to realizing highly-transparent
topological Josephson junctions, and show how the response of superconducting
systems to microwave radiation can be used to infer the dynamics of phase-slip
lines.
