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We determine the Weierstrass semigroup $H(P_\infty,P_1,\ldots,P_m)$ atseveral rational points on the maximal curves which cannot be covered by theHermitian curve introduced by Tafazolian, Teher\'an-Herrera, and Torres.Furthermore, we present some conditions to find pure gaps. We use thissemigroup to obtain AG codes with better relative parameters than comparableone-point AG codes arising from these curves.

Weierstrass semigroup at $m+1$ rational points in maximal curves which cannot be covered by the Hermitian curve