  We investigate effects of the modified $f(R, \mathcal{T})$ gravity on the
charged strange quark stars with the standard choice of $f(R,
\mathcal{T})=R+2\chi \mathcal{T}$. Those types of stars are supposed to be made
of strange quark matter (SQM) whose distribution is governed by the
phenomenological MIT bag EOS as $p=\frac{1}{3}(\rho-4B)$, where $B$ is the bag
constant, while the form of charge distribution is chosen to be
$q\left(r\right)=Q\left(r/R\right)^3=\alpha r^3$ with $\alpha$ as a constant.
We derive the values of the unknown parameters by matching the interior
spacetime to the exterior Reissner-Nordstr{\"o}m metric followed by the
appropriate choice of the values of the parameters $\chi$ and $\alpha$. Our
study reveals that besides SQM, a new kind of matter distribution originates
due to the interaction between the matter and the extra geometric term, while
the modification of the Tolman-Oppenheimer-Volkoff (TOV) equation invokes the
presence of a new force $F_c$. The accumulation of the electric charge
distribution reaches its maximum at the surface, and the predicted values of
the corresponding electric charge and electric field are of the order of
$10^{19-20}$ C and $10^{21-22}$ V/cm, respectively. To examine the physical
validity of our solutions, we perform several tests and find that the proposed
$f(R, \mathcal{T})$ model survives all these critical tests. Therefore, our
model can describe the non-singular charged strange stars and justify the
supermassive compact stellar objects having their masses beyond the maximum
mass limit for the compact stars in the standard scenario. Our model also
supports the existence of several exotic astrophysical objects like
super-Chandrasekhar white dwarfs, massive pulsars, and even magnetars, which
remain unexplained in the framework of General Relativity (GR).
