Superconducting topological crystalline insulators (TCIs) have been proposed to be a new type of topological superconductor where multiple Majorana zero modes may coexist under the protection of lattice symmetries. The bulk superconductivity of TCIs has been realized, but it is quite challenging to detect the superconductivity of topological surface states inside their bulk superconducting gaps. Here, we report high-resolution scanning tunneling spectroscopy measurements on lateral Sn_{1-x}Pb_{x}Te-Pb heterostructures using superconducting tips. Both the bulk superconducting gap and the multiple in-gap states with energy differences of ∼0.3 meV can be clearly resolved on TCI Sn_{1-x}Pb_{x}Te at 0.38 K. Quasiparticle interference measurements further confirm the in-gap states are gapless. Our work demonstrates that the unique topological superconductivity of a TCI can be directly distinguished in the density of states, which helps to further investigate the multiple Dirac and Majorana fermions inside the superconducting gap.