  In this work, we investigate the existence of neutron stars (NS) in the
framework of $f$($\mathbb{T}$,$\mathcal{T}$) gravity, where $\mathbb{T}$ is the
torsion tensor and $\mathcal{T}$ is the trace of the energy-momentum tensor.
The hydrostatic equilibrium equations are obtained, however, with $p$ and
$\rho$ quantities passed on by effective quantities $\bar{p}$ and $\bar{\rho}$,
whose mass-radius diagrams are obtained using modern equations of state (EoS)
of nuclear matter derived from relativistic mean field models and compared with
the ones computed by the Tolman-Oppenheimer-Volkoff (TOV) equations.
Substantial changes in the mass-radius profiles of NS are obtained even for
small changes in the free parameter of this modified theory. The results
indicate that the use of $f$($\mathbb{T}$,$\mathcal{T}$) gravity in the study
of NS provides good results for the masses and radii of some important
astrophysical objects, as for example, the low-mass X-ray binary (LMXB) NGC
6397 and the pulsar of millisecond PSR J0740+6620. In addition, radii results
inferred from the Lead Radius EXperiment (PREX-2) can also be described for
certain parameter values.
