  In this work, we investigate some extensions of the Kiselev black hole
solutions in the context of $f(\mathbb{T},\CMcal{T})$ gravity. By mapping the
components of the Kiselev energy-momentum tensor into the anisotropic
energy-momentum tensor and assuming a particular form of
$f(\mathbb{T},\CMcal{T})$, we obtain exact solutions for the field equation in
this theory that carries dependence on the coupling constant and on the
parameter of the equation of state of the fluid. We show that in this scenario
of modified gravity some new structure is added to the geometry of spacetime as
compared to the Kiselev black hole. We analyse the energy conditions, mass,
horizons and the Hawking temperature considering particular values for the
parameter of the equation of state.
