  Discovery of exotic phases of matter from the topologically non-trivial
systems not only makes the research on topological materials more interesting
but also enriches our understanding of the fascinating physics of such
materials. Pb$_{0.6}$Sn$_{0.4}$Te was recently shown to be a topological
crystalline insulator. Here we show that by forming a mesoscopic point-contact
using a normal non-superconducting elemental metal on the surface of
Pb$_{0.6}$Sn$_{0.4}$Te a novel superconducting phase is created locally in a
confined region under the point-contact. This happens while the bulk of the
sample remains to be non-superconducting and the superconducting phase emerges
as a nano-droplet under the point-contact. The superconducting phase shows a
high transition temperature $T_c$ that varies for different point-contacts and
falls in a range between 3.7 K and 6.5 K. Therefore, this Letter presents the
discovery of a new superconducting phase on the surface of a topological
crystalline insulator and the discovery is expected to shed light on the
mechanism of induced superconductivity in topologically non-trivial systems in
general.
