  We study the emergence of interfacial modes between the two regions of a
semi-Dirac type material, which are illuminated by the left and right
circularly polarized light, respectively. We show that a smooth boundary
between the two regions give rise to an interfacial quantum well which is
sensitive to the incoming electron's momentum. The quantum well is found to
host the Volkov-Pankratov states which are gapless metallic in nature. Contrary
to the inverted mass term, it is the inverted velocity term that induces such
states across the boundary. We also note that incident electron can fully pass
over the interfacial well without any reflection only at certain light
parameters-known as {\it Ramsauer-Townsend} effect. Moreover, we also observe
that such modes can even exist across the interface between the irradiated and
non-irradiated regions under certain condition.
