  This article investigates on the radial and non-radial geodesic structures of
the generalized K-essence Vaidya spacetime. Within the framework of K-essence
geometry, it is important to note that the metric does not possess conformal
equivalence to the conventional gravitational metric. This study employs a
non-canonical action of the Dirac-Born-Infeld kind. In this work, we categorize
the generalized K-essence Vaidya mass function into two distinct forms. Both
the forms of the mass functions have been extensively utilized to analyze the
radial and non-radial time-like or null geodesics in great details inside the
comoving plane. Indications of the existence of wormhole can be noted during
the extreme phases of spacetime, particularly in relation to black holes and
white holes, which resemble the Einstein-Rosen bridge. In addition, we have
also detected the distinctive indication of the quantum tunneling phenomenon
around the central singularity.
