  We investigate inflationary models in f(R,T) modified gravity with a kinetic
coupling term \omega^2 G^{\mu\nu}\partial_{\mu}\phi\partial_{\nu}\phi having a
positive factor needed to remove the ghosts. Taking f(R,T)=R+2\beta T, we
calculate and analyse the relevant observable quantities including the spectral
index $n_s$ and the tensor-to-scalar ratio r using the slow-roll
approximations. Concretely, we consider two scenarios described by the
decoupling and the coupling behaviors between the scalar potential and the
f(R,T) gravity via the moduli space by dealing with two potentials being the
quartic one V(\phi) =\lambda \phi^4 and the small field inflation V(\phi)
=V_0(1- (\frac{\phi}{\mu})^\alpha). For the quartic inflation model, we
consider a decoupling behavior. For the small field inflation, however, we
present the parameter decoupling and coupling scenarios. For both scenarios, we
compute and inspect n_s and r showing interesting results. For three different
values of the number of e-folds N=60,65 and 70, we find that the coupling
between f(R,T)1 and the scalar potential via the moduli space provides an
excellent agreement with the observational findings. In the last part of this
work, we provide a possible discussion on the amplitude of scalar power
spectrum needed to provide a viability of the proposed theory. Considering the
second potential form in the parameter coupling scenario, we find acceptable
values in certain points of the moduli space.
