AbstractTopological superconductivity is central to a variety of novel phenomena involving the interplay between topologically ordered phases and broken-symmetry states. The key ingredient is an unconventional order parameter, with an orbital component containing a chiral p _x + ip _y wave term. Here we present phase-sensitive measurements, based on the quantum interference in nanoscale Josephson junctions, realized by using Bi₂Te₃ topological insulator. We demonstrate that the induced superconductivity is unconventional and consistent with a sign-changing order parameter, such as a chiral p _x + ip _y component. The magnetic field pattern of the junctions shows a dip at zero externally applied magnetic field, which is an incontrovertible signature of the simultaneous existence of 0 and π coupling within the junction, inherent to a non trivial order parameter phase. The nano-textured morphology of the Bi₂Te₃ flakes, and the dramatic role played by thermal strain are the surprising key factors for the display of an unconventional induced order parameter.