  In this paper, we reconsider the mixed system of BSs with wormholes at their
center which performed by complex scalar field and phantom field and study a
whole new condition about the potential. Both the symmetric and asymmetric
solutions in the two asymptotically flat regions are obtained by using
numerical method and we mainly explore the change of the results by varying the
parameters of throats and potential. In ground state, we find there are
multiple solutions at certain setting of parameters and with the increase of
$\eta_0$ or decrease of $c$, the results gradually become single-valued
functions and these two variables have similar influence to the curve shape of
mass $M$ and charge $Q$, furthermore, the asymmetric solutions can turn into
the solutions of symmetry at some frequency $\omega$ in certain $\eta_0$ and
$c$. However, when it comes to excited state, the properties of solutions of
symmetry is similar to the ground state while asymmetrical results exhibit
altered characteristics. We also present the geometries of wormhole to
investigate the property of this model.
