We give details about how a surface plasmons with phase singularities can be produced when a Bessel beam light is totally reflected internally at the planar surface of a dielectric on which an infinitesimally thin film has been deposited. The characteristic property of such a light is the exponential decay with distance in a vacuum which can basically provide a two-dimensional surface plasmons with phase singularities with attractive enhancements. Such a phenomenon is governable by altering the incident angle and the order of the Bessel beam.