In the search for Majorana fermions in proximity-induced topological superconducting junctions, we happened to find a signature of same-spin triplet superconductivity which appears to dominate these elusive elementary excitations. Thin-film junctions and bilayers of the doped topological insulator and the s-wave superconductor NbN exhibit conductance spectra with coexisting prominent zero-bias and coherence peaks. Various tunneling models with different pair potentials have failed to fit our data, except for the triplet pair potential, which breaks time-reversal symmetry, that yielded reasonably good fits. This provides supporting evidence for proximity-induced triplet superconductivity in the layer near the interface with the NbN film.