  Teleparallel based cosmological models provide a description of gravity in
which torsion is the mediator of gravitation. Several extensions have been made
within the so-called Teleparallel equivalent of general relativity which is
equivalent to general relativity at the level of the equations of motion where
attempts are made to study the extensions of this form of gravity and to
describe more general functions of the torsion scalar $T$. One of these
extensions is $f(T,\phi)$ gravity; $T$ and $\phi$ respectively denote the
torsion scalar and scalar field. In this work, the dynamical system analysis
has been performed for this class of theories to obtain the cosmological
behaviour of a number of models. Two models are presented here with some
functional form of the torsion scalar and the critical points are obtained. For
each critical point, the stability behaviour and the corresponding cosmology
are shown. Through the graphical representation the equation of state parameter
and the density parameters for matter-dominated, radiation-dominated and dark
energy phase are also presented for both the models.
