[en] MoTe₂ is a Weyl semimetal, which exhibits unique non-saturating magnetoresistance and strongly reinforced superconductivity under pressure. Here, we demonstrate that a novel mesoscopic superconductivity at ambient pressure arises on the surface of MoTe₂ with a critical temperature up to 5 K significantly exceeding the bulk T _c  =  0.1 K. We measured the derivatives of I–V curves for hetero-contacts of MoTe₂ with Ag or Cu, homo-contacts of MoTe₂ as well as ‘soft’ point contacts (PCs). Large number of these hetero-contacts exhibit a dV/dI dependence, which is characteristic for Andreev reflection. It allows us to determine the superconducting gap Δ. The average gap values are 2Δ  =  1.30  ±  0.15 meV with a 2Δ/k _B T _c ratio of 3.7  ±  0.4, which slightly exceeds the standard BCS value of 3.52. Furthermore, the temperature dependence of the gap follows a BCS-like behavior, which points to a nodeless superconducting order parameter with some strong-coupling renormalization. Remarkably, the observation of a ‘gapless-like’ single minimum in the dV/dI of ‘soft’ PCs may indicate a topological superconducting state of the MoTe₂ surface as these contacts probe mainly the interface and avoid additional pressure effect. Therefore, MoTe₂ might be a suitable material to study new forms of topological superconductivity. (paper)