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In this work we determine the so-called minimal generating set of theWeierstrass semigroup of certain $m$ points on curves $\mathcal{X}$ with planemodel of the type $f(y) = g(x)$ over $\mathbb{F}_{q}$, where $f(T),g(T)\in\mathbb{F}_q[T]$. Our results were obtained using the concept of discrepancy,for given points $P$ and $Q$ on $\mathcal{X}$. This concept was introduced byDuursma and Park, in \cite{duursma}, and allows us to make a different and moregeneral approach than that used to certain specific curves studied earlier.

On Weierstrass semigroup at $m$ points on curves of the type f(y) = g(x)