  In this paper, we study the spherically symmetric Dirac star model in the
presence of a phantom field, obtaining a traversable wormhole solution in
non-trivial topological spacetime. This solution exhibits asymmetry in both the
field configuration and the metric and possesses a finite ADM mass $M$ and
Noether charge $Q$. Furthermore, we find that due to the presence of a wormhole
at the center, this solution exhibits many differences from the Dirac star
under trivial spacetime. Notably, when the wormhole throat size is small, our
numerical calculations indicate the emergence of an extremely approximate black
hole solution on one side of the wormhole spacetime, a phenomenon unexplored.
At this time, the Kretschmann scalar near the throat tends to infinity,
indicating the wormhole becomes untraversable.
