Exploring the cosmological model in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e948" altimg="si15.svg"><mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>R</mml:mi><mml:mo>,</mml:mo><mml:msup><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>ϕ</mml:mi></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> gravity with observational constraints

We have investigated an isotropic and homogeneous cosmological model of the universe in $f(R, T^{\phi})$ gravity, where $T^{\phi}$ is trace energy-momentum tensor $R$ Ricci scalar. developed presented exact solutions field equations proposed by taking parametrization $q(z) =\alpha + \frac{\beta z}{1+z}$, $\alpha$ $\beta$ are arbitrary constants. The best possible values model's free parameters estimated using latest observational data sets OHD, BAO, Pantheon applying MCMC statistical technique. Some kinematic properties like density parameter $\rho_{\phi}$, pressure $p_{\phi}$, equation state $\omega_{\phi}$ derived. also discussed behavior scalar potential $V(\phi)$ gravity theory. behaviors fields for quintessence phantom models explored. Furthermore, we energy conditions sound speed cosmology.