  The homogeneous and isotropic cosmological model in generalized $ f(R,T^\phi)
$ theories associated with scalar field is discussed, which is motivated by the
$ f(R,T) $ theory of gravity studied by Harko et al. \cite{Harko:2011kv,
Harko:2014pqa}. The $ f(R,T^\phi) $ gravity can be explained as $ f(R,T) $
gravity with a self-interacting scalar field $ \phi $, where $ T^\phi $ is the
trace of the energy-momentum tensor. The parametrization of Hubble parameter $
H(t) $ is taken as $ \alpha-\beta e^{-\gamma t} $, where $ \alpha $, $\beta$
and $\gamma$ are arbitrary constants such that $ \alpha, \gamma>0 $ and $
\beta<0 $. The model shows no space-time singularity and the expansion of the
universe will continue forever, i.e., the future scenario of the universe
attains Big Freeze. The model predicts the moderate inflationary scenario at
the time of the evolution of the universe and it is consistent with $ \Lambda
$CDM in late times. The consistency of the model has also been examined using
recent observational Hubble dataset and supernovae dataset. Finally, the
physical features of the model have been discussed in some detail.
