In the context of quintessence, the inclusion of new degrees of freedoms to the matter sector might produce additional imprints on cosmological observables while keeping the scalar field responsible for the quintessence and the standard matter minimally coupled to gravity. We investigate this premise by including a canonical SU(2) Yang-Mills field to the total content of the universe coupled to the standard quintessencial field by a disformal transformation. The effects of the gauge field are studied in an anisotropic background configuration in order to allow for more general outcomes. The background dynamics study is addressed by a dynamical system analysis from which novel anisotropic scaling solutions with a non-vanishing gauge field are obtained. After establishing the dynamical character of the fixed points, the phenomenological consequences of the model are assessed by means of a numerical analysis. An interesting result to be confronted with observations is a transient matter-radiation phase for the gauge field dynamics. We have also quantified the redshift-dependent contribution of the gauge field in the form of dark radiation during the radiation era to the effective number of relativistic species. This depends essentially on the initial conditions and, more importantly, on the disformal coupling function. Phenomenological couplings and the Abelian version of the model are discussed as well to check the generality of our results.
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