P*

The advent of topological insulators (TIs) in a three-dimensional system followed by topological semimetallic states (TSMs) brought a paradigm shift in the understanding of the materials. Here we report the observation of the surface Dirac dispersion in a material Ti₂Te₂P at the M point of the Brillouin zone (BZ) in a tetradymite crystal structure employing angle-resolved photoemission spectroscopy (ARPES), which is in agreement with the first-principles calculations. Our study further reveals a Dirac cone dispersion at the Gamma-point of the BZ suggesting that this material holds multi-fermionic states. Our systematic studies open a platform to study the exotic properties of Dirac state in a single material.