  In this current study, our main focus is to model a specific charged compact
star SAX J 1808.4-3658 (M = 0.88 $M_{\odot}$,\, R = 8.9 km) within the realm of
$f(R,\,T)$ modified gravity theory using the metric potentials proposed by
Tolman-Kuchowicz (Tolman, Phys Rev 55:364, 1939; Kuchowicz Acta Phys Pol
33:541, 1968) and the interior spacetime is matched to the exterior
Reissner-Nordstr\"{o}m line element at the surface of the star.
Tolman-Kuchowicz metric potentials provide a singularity-free solution which
satisfies the stability criteria. Here we have used the simplified
phenomenological MIT bag model equation of state (EoS) to solve
Einstein-Maxwell field equations where the density profile ($\rho$) is related
to the radial pressure ($p_r$) as $p_r(r) = (\rho - 4B_g)/3$. Further, to
derive the values of unknown constants $a,\, b,\, B,\, C$ and the bag constant
$B_g$, we match our interior space-time to the exterior Reissner-Nordstr\"{o}m
line element at the surface of stellar system. In addition to this, to check
the physical validity and stability of our suggested model, we evaluate some
important properties such as effective energy density, effective pressures,
radial and transverse sound velocities, relativistic adiabatic index, all
energy conditions, compactness factor and surface redshift. It is depicted from
our current study that all our derived results lie within the physically
accepted regime which provides the viability of our present model in the
context of $f(R,\,T)$ modified gravity.
