  WTe$_2$ is a layered transitional-metal dichalcogenide (TMD) with a number of
intriguing topological properties. Recently, WTe$_2$ has been predicted to be a
higher-order topological insulator (HOTI) with topologically protected hinge
states along the edges. The gapless nature of WTe$_2$ complicates the
observation of one-dimensional (1D) topological states in transport due to
their small contribution relative to the bulk. Here, we study the behavior of
the Josephson effect in magnetic field to distinguish edge from bulk transport.
The Josephson effect in few-layer WTe$_2$ reveals 1D states residing on the
edges and steps. Moreover, our data demonstrates a combination of Josephson
transport properties observed solely in another HOTI - bismuth, including
Josephson transport over micrometer distances, extreme robustness in a magnetic
field, and nonsinusoidal current-phase relation (CPR). Our observations
strongly suggest the topological origin of the 1D states and that few-layer
WTe$_2$ is a HOTI.
