  Proximity-induced superconductivity in three dimensional (3D) topological
insulators forms a new quantum phase of matter and accommodates exotic
quasiparticles such as Majorana bound states. One of the biggest drawbacks of
the commonly studied 3D topological insulators is the presence of conducting
bulk that obscures both surface states and low energy bound states. Introducing
superconductivity in topological Kondo insulators such as SmB$_6$, however, is
promising due to their true insulating bulk at low temperatures. In this work,
we develop an unconventional Josephson junction by coupling superconducting Nb
leads to the surface states of a SmB$_6$ crystal. We observe a robust critical
current at low temperatures that responds to the application of an out-of-plane
magnetic field with significant deviations from usual Fraunhofer patterns. The
appearance of Shaphiro steps under microwave radiation gives further evidence
of a Josephson effect. Moreover, we explore the effects of Kondo breakdown in
our devices, such as ferromagnetism at the surface and anomalous temperature
dependence of supercurrent. Particularly, the magnetic diffraction patterns
show an anomalous hysteresis with the field sweep direction suggesting the
coexistence of magnetism with superconductivity at the SmB$_6$ surface. The
experimental work will advance the current understanding of topologically
nontrivial superconductors and emergent states associated with such
unconventional superconducting phases.
