  In this article, we explore the concept of cosmological inflation within the
framework of the $f (T,\mathcal{T})$ theory of gravity, where $f$ is a general
function of the Torsion scalar $T$ and the trace, $\mathcal{T}$, of the
energy-momentum tensor. It is assumed that the conditions of slow-roll
inflation are applicable in$f (T,\mathcal{T})$ gravity. To determine different
observables related to inflation, such as the tensor-to-scalar ratio $r$,
scalar spectral index $n_s$, spectral index $ \alpha_s $, and tensor spectral
index $n_t$, the Hubble slow-roll parameters are utilized for a particular
model of $f (T,\mathcal{T})$. Lastly, an assessment has been carried out to
determine the feasibility of the models by conducting a numerical analysis of
the parameters. The findings indicate that it is feasible to achieve
compatibility with the observational measurements of slow-roll parameters by
utilizing different values of the free parameters.
