We establish a Riesz potential criterion for Lebesgue continuity points of functions of bounded |$\mathbb{A}$| -variation, where |$\mathbb{A}$| is a |$\mathbb{C}$| -elliptic differential operator of arbitrary order. This result generalizes a potential criterion that is known for full gradients to the case where full gradient estimates are not available by virtue of Ornstein's non-inequality.