  We study the Seshadri constants of cyclic coverings of smooth surfaces. The
existence of an automorphism on these surfaces can be used to produce Seshadri
exceptional curves. We give a bound for multiple Seshadri constants on cyclic
coverings of surfaces with Picard number 1. Morevoer, we apply this method to
$n$-cyclic coverings of the projective plane. When $2\leq n\leq 9$, explicit
values are obtained. We relate this problem with the Nagata conjecture.
