  We study strange stars in the framework of $f\left(R,\mathcal{T}\right)$
theory of gravity where the strange quark matter distribution inside the
stellar system is governed by the phenomenological MIT Bag model equation of
state (EOS). Further, for a specific value of $B$ and observed values of mass
of the strange star candidates we obtain the exact solution of the modified
Tolman-Oppenheimer-Volkoff (TOV) equation in the framework of
$f\left(R,\mathcal{T}\right)$ gravity and have studied in detail the dependence
of the different physical parameters due to the chosen different values of
$\chi$. To check the physical acceptability and stability of the stellar system
based on the obtained solutions we have performed different physical tests,
viz., the energy conditions, Herrera cracking concept, adiabatic index etc. In
this work, we also have explained the effects, those are arising due to the
interaction between the matter and the curvature terms in
$f\left(R,\mathcal{T}\right)$ gravity, on the anisotropic compact stellar
system. It is interesting to note that as the values of $\chi$ increase the
strange stars become more massive and their radius increase gradually so that
eventually they gradually turn into less dense compact objects. The present
study reveals that the modified $f\left(R,\mathcal{T}\right)$ gravity is a
suitable theory to explain massive stellar systems like recent magnetars,
massive pulsars and super-Chandrasekhar stars, which can not be explained in
the framework of GR. However, for $\chi=0$ the standard results of Einsteinian
gravity are retrieved.
