Combining multiple emergent correlated properties such as superconductivity and magnetism within the topological matrix can have exceptional consequences in garnering new and exotic physics. Here, we study the topological surface states from a noncentrosymmetric α-BiPd superconductor by employing angle-resolved photoemission spectroscopy and first-principles calculations. We observe that the Dirac surface states of this system have several interesting and unusual properties, compared to other topological surface states. The surface state is strongly anisotropic and the in-plane Fermi velocity varies rigorously on rotating the crystal about the y axis. Moreover, it acquires an unusual band gap as a function of k_{y}, possibly due to hybridization with bulk bands, detected upon varying the excitation energy. The coexistence of all the functional properties in addition to the unusual surface state characteristics make this an interesting material.