  The noncentrosymmetric Td-WTe$_2$, previously known as a type-II Weyl
semimetal, is expected to have higher order topological phases with
topologically protected, helical one-dimensional (1D) hinge states when their
scarcely separated Weyl points get annihilated. However, the detection of these
hinge states is difficult in the presence of the semimetallic behaviour of the
bulk. Here, we spatially resolved the hinge states by analysing the magnetic
field interference of supercurrent in Nb-WTe$_2$-Nb proximity Josephson
junctions. The Josephson current along the a-axis of the WTe$_2$ crystal, but
not along the b-axis, showed sharp enhancements at the edges of the junction;
the amount of enhanced Josephson current was comparable to the upper limits of
a single 1D conduction channel. Our experimental observations provide evidence
of the higher order topological phase in WTe$_2$ and its corresponding
anisotropic topological hinge states, in good agreement with theoretical
calculations. Our work paves the way for hinge transport studies on topological
semimetals in superconducting heterostructures, including their topological
superconductivity.
