In 2017, D. Skabelund constructed a maximal curve over Fq4​ as
a cyclic cover of the Suzuki curve. In this paper we explicitly determine the
structure of the Weierstrass semigroup at any point P of the Skabelund curve.
We show that its Weierstrass points are precisely the
Fq4​-rational points. Also we show that among the Weierstrass
points, two types of Weierstrass semigroup occur: one for the
Fq​-rational points, one for the remaining
Fq4​-rational points. For each of these two types its Ap\'ery set
is computed as well as a set of generators