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A class of α-potentials represented as the sum of modified Green potential and modified Poisson integral are proved to have the growth estimates Rα,l,l(x)=o(xnβ|x|l−2β+2h(|x|)−1) at infinity in the upper-half space of the n-dimensional Euclidean space, where the function h(|x|) is a positive non-decreasing function on the interval (0,∞) satisfying certain conditions. This result generalizes the growth properties of analytic functions, harmonic functions, and superharmonic functions.