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Many physically inspired general relativity (GR) modifications predict
significant deviations in the properties of spacetime surrounding massive
neutron stars. Among these modifications is $f(\mathcal{R}, \mathbb{T})$, where
$\mathcal{R}$ is the Ricci scalar, $\mathbb{T}$ represents the trace of the
energy-momentum tensor, the gravitational theory that is thought to be a
neutral extension of GR. Neutron stars with masses above 1.8 $M_\odot$
expressed as radio pulsars are precious tests of fundamental physics in extreme
conditions unique in the observable universe and unavailable to terrestrial
experiments. We obtained an exact analytical solution for spherically symmetric
anisotropic perfect-fluid objects in equilibrium hydrostatic using the frame of
the form of $f(\mathcal{R},\mathbb{T})=\mathcal{R}+\beta \mathbb{T}$ where
$\beta$ is a dimensional parameter. We show that the dimensional parameter
$\beta$ and the compactness, $C=\frac{ 2GM}{Rc^2}$ can be used to express all
physical quantities within the star. We fix the dimensional parameter $\beta$
to be at most. (Here ${\mathrm \kappa^2}$ is the coupling constant of Einstein
which is figured as $\kappa^2=\frac{8\pi G}{c^4}$, the Newtonian constant of
gravitation is denoted as $G$ while $c$ represents the speed of light.)
$\beta_1=\frac{\beta}{\kappa^2}= 0.1$ in positive values through the use of
observational data from NICER and X-ray Multi-Mirror telescopes on the pulsar
PSR J0740+6620, which provide information on its mass and radius.