Generalized Weierstrass semigroups at several points on certain maximal curves which cannot be covered by the Hermitian curve

In this paper we determine the generalized Weierstrass semigroup \( \widehat{H}(P_{\infty}, P_1, \ldots , P_{m})\), and consequently the Weierstrass semigroup \(H(P_{\infty}, P_1, \ldots , P_{m})\), at \(m+1\) points on the curves \(\mathcal{X}_{a,b,n,s}\) and \(\mathcal{Y}_{n,s}\). These curves has been introduced in Tafazolian et al. as new examples of curves which cannot be covered by the Hermitian curve.