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In 2017, D. Skabelund constructed a maximal curve over $\mathbb{F}_{q^4}$ asa cyclic cover of the Suzuki curve. In this paper we explicitly determine thestructure of the Weierstrass semigroup at any point $P$ of the Skabelund curve.We show that its Weierstrass points are precisely the$\mathbb{F}_{q^4}$-rational points. Also we show that among the Weierstrasspoints, two types of Weierstrass semigroup occur: one for the$\mathbb{F}_q$-rational points, one for the remaining$\mathbb{F}_{q^4}$-rational points. For each of these two types its Ap\'ery setis computed as well as a set of generators.

Weierstrass semigroups on the Skabelund maximal curve