  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 $\alpha$-BiPd superconductor by employing
angle-resolved photoemission spectroscopy (ARPES) and first principle
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.
Coexistence of all the functional properties, in addition to the unusual
surface state characteristics make this an interesting material.
