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We study $p$-group Galois covers $X \rightarrow \mathbb{P}^1$ with only onefully ramified point. These covers are important because of the Katz-Gabbercompactification of Galois actions on complete local rings. The sequence oframification jumps is related to the Weierstrass semigroup of the global coverat the stabilized point. We determine explicitly the jumps of the ramificationfiltrations in terms of pole numbers. We give applications for curves with zero$p$--rank: we focus on maximal curves and curves that admit a big action.  Moreover the Galois module structure of polydifferentials is studied and anapplication to the tangent space of the deformation functor of curves withautomorphisms is given.

Automorphisms of Curves and Weierstrass semigroups for Harbater-Katz-Gabber covers