Recent instrumentation and computational advances have increased interest in determining the properties of nuclear matter under extreme conditions and the core of neutron stars (NSs) is an excellent test bed for nuclear astrophysical theories. Moreover, the detection of pulsars heavier than 2 M ⊙ have put strong constraints on the NS matter equation of state (EoS), and consequently the interior composition. Here, we investigate compact static configurations whose matter field is comprised of homogeneous, neutral 3-flavor interacting quark matter with O ( m s 4 ) corrections, namely, interacting quark EoS in the context of f ( R , T ) gravity theories. The EoS consists of the bag constant B and the interaction parameter a 4 that plays an important role in the construction of a quark star model. Numerical computations are required to solve the structure equations and to derive the mass–radius relation for a given equation of state. In addition, we employ the maximum mass from two pulsars PSR J0348+0432 and PSR J0751+1807 as an input for inferring the dense matter EoS. Our finding allows us to explain some observational facts more efficiently than in standard General Relativity.