In this work, we have obtained new phantom fluid-type traversable wormhole (WH) solutions in the context of \(f(\mathcal {R}, T)\) modified gravity. We investigate the potential that some equations of state (EoS), specifically phantom energy, which describes the accelerated expansion of the universe, could support the existence of traversable wormholes. This cosmic fluid thus offers us a plausible explanation for the occurrence of WH geometries. We construct two WH models with matter Lagrangian density \(\mathcal {L}_{m}=-(-\rho +\mathcal {P}_{r}+2\mathcal {P}_{t})\) and inspect numerous characteristics of these models under the WH geometry. The first WH solution (WH-I) is discovered by utilising a linear barotropic equation of state (EoS) connected with phantom energy \(\omega <-1\) indicating the presence of the phantom fluid and pointing to the Universe’s expansion, while in the second WH (WH-II) solution, we take into account an interesting EoS \(\rho =\eta (\mathcal {P}_{t}-\mathcal {P}_{r})\) to generate a WH model. Additionally, it showed that the phantom fluid WH-I solution violates the radial null energy condition (NEC) while tangential NEC is satisfied. On the other hand, for the WH-II solution, NEC is violated. Extensive detailed discussions of the matter components have been done via graphical analysis. The obtained WH geometries satisfy a stable WH’s physically acceptable criteria.
