  Recent advances in nuclear theory combined with new astrophysical
observations have led to the need for specific theoretical models that actually
apply to phenomena on dense-matter physics. At the same time, quantum
chromodynamics (QCD) predicts the existence of non-nucleonic degrees of freedom
at high densities in neutron-star matter, such as quark matter. Within a
confining quark matter model, which consists of homogeneous, neutral 3-flavor
interacting quark matter with $\mathcal{O}(m_s^4)$ corrections, we study the
structure of compact stars made of a charged perfect fluid in the context of
$f(R,T)$ gravity. The system of differential equations that describe the
structure of charged compact stars have been derived and solved numerically for
a gravity model with $f(R,T)= R+ 2\beta T$. For simplicity, we assume that the
charge density is proportional to the energy density, namely, $\rho_{\rm ch} =
\alpha \rho$. It is demonstrated that matter-geometry coupling constant $\beta$
and the charge parameter $\alpha$ affect the total gravitational mass and the
radius of the star.
