  We consider extended covariant teleparallel $(f(T))$ gravity whose action is
analytic in the torsion scalar and which is sourced by an $su(2)$ valued
Yang-Mills field. Specifically, we search for regular solutions to the coupled
$f(T)$ Yang-Mills system. For $f(T)=T$ we, not surprisingly, recover the
Bartnik-McKinnon solitons of Einstein Yang-Mills theory. However, interesting
effects are discovered with the addition of terms in the action which are
nonlinear in the torsion scalar, which we specifically study up to cubic order.
With the addition of the nonlinear terms the number of regular solutions
becomes finite. As well, beyond critical values of the coupling constants we
find that there exist \emph{no} regular solutions. These behaviors are
asymmetric with respect to the sign of the nonlinear coupling constants and the
elimination of regular solutions turns out to be extremely sensitive to the
presence of the cubic coupling. It may be possible, therefore, that with
sufficiently high powers of torsion in the action, there may be no regular
Yang-Mills static solutions.
