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WTe₂ is a layered material with rich topological properties. The bulk crystal is a type-II Weyl semimetal and the monolayer is a two-dimensional topological insulator. Recently, it has been predicted that higher order topological insulator state can appear in WTe₂. An observation of 1D, highly conductive channels, known in this case as hinge states, is hindered by the bulk conductivity of WTe₂. Here, we employ the Josephson effect to disentangle the contribution of the hinge states from the bulk in electronic transport. We observe 1D current carrying states on edges and steps in few-layer WTe₂. The width of the states is deduced to be below 100 nm. A supercurrent in them can be measured over distances up to 3 µm and in perpendicular magnetic field up to 2 T. Moreover, the dependence of the supercurrent on the magnetic field is compatible with the asymmetric Josephson effect predicted to occur in topological systems with broken inversion symmetry.