  A finite group with a Beauville structure gives rise to a certain compact
complex surface called a Beauville surface. G\"{u}l and Uria-Albizuri showed
that quotients of the periodic Grigorchuk-Gupta-Sidki (GGS-)groups that act on
the $p$-adic tree, for $p$ an odd prime, admit Beauville structures. We extend
their result by showing that quotients of infinite periodic GGS-groups acting
on $p^n$-adic trees, for $p$ any prime and $n\ge 2$, also admit Beauville
structures.
