  Within this work, we propose a new generalised quintom dark energy model in
the teleparallel alternative of general relativity theory, by considering a
non-minimal coupling between the scalar fields of a quintom model with the
scalar torsion component $T$ and the boundary term $B$. In the teleparallel
alternative of general relativity theory, the boundary term represents the
divergence of the torsion vector, $B=2\nabla_{\mu}T^{\mu}$, and is related to
the Ricci scalar $R$ and the torsion scalar $T$, by the fundamental relation:
$R=-T+B$. We have investigated the dynamical properties of the present quintom
scenario in the teleparallel alternative of general relativity theory by
performing a dynamical system analysis in the case of decomposable exponential
potentials. The study analysed the structure of the phase space, revealing the
fundamental dynamical effects of the scalar torsion and boundary couplings in
the case of a more general quintom scenario. Additionally, a numerical approach
to the model is presented to analyse the cosmological evolution of the system.
