[en] We define the worldline harmonic $SU(2|1)$ superspace and its analytic subspace as a deformation of the flat $\mathcal{N}=4,d=1$ harmonic superspace. The harmonic superfield description of the two mutually mirror off-shell $(\mathbf{4},\mathbf{4},\mathbf{0})SU(2|1)$ supermultiplets is developed and the corresponding invariant actions are presented, as well as the relevant classical and quantum supercharges. Whereas the σ-model actions exist for both types of the $(\mathbf{4},\mathbf{4},\mathbf{0})$ multiplet, the invariant Wess–Zumino term can be defined only for one of them, thus demonstrating non-equivalence of these multiplets in the $SU(2|1)$ case as opposed to the flat $\mathcal{N}=4,d=1$ supersymmetry. A superconformal subclass of general $SU(2|1)$ actions invariant under the trigonometric-type realizations of the supergroup $D(2,1;\mathrm{\alpha <!--\; ??\; -->})$ is singled out. The superconformal Wess–Zumino actions are shown to possess an infinite-dimensional supersymmetry forming the centerless $\mathcal{N}=4$ super Virasoro algebra. We solve a few simple instructive examples of the $SU(2|1)$ supersymmetric quantum mechanics of the $(\mathbf{4},\mathbf{4},\mathbf{0})$ multiplets and reveal the $SU(2|1)$ representation contents of the corresponding sets of the quantum states. (paper)