  We present the first interior solutions representing compact stars in
$\kappa(\mathcal{R},\mathcal{T})$ gravity, by solving the modified field
equations in isotropic coordinates. Further, we have assumed the metric
potentials in Schwarzschild's form and a few parameters along with the
isotropic condition of pressure. For solving, we use specific choice of the
running gravitational constant as $\kappa(\mathcal{R},\mathcal{T})=8\pi-\lambda
\mathcal{T} ~~(G=\tilde{c}=1)$. Once arrived at the reduced field equations, we
investigate two solutions with $c=1$ and $c \neq 1$, where $c$ denotes here
another constant that should not be confused with the speed of light. Then, we
investigate each solution by determining the thermodynamics variable {\it viz}
pressure, density, speed of sound, and adiabatic index. We found that these
solutions satisfy the Bondi criterion, causality condition, and energy
conditions. We also found that the $M-R$ curves generated from these solutions
satisfy the stringent constraints provided by the gravitational wave
observations due to the neutron star merger GW 170817.
