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Let $F$ be a totally real field of even degree in which $p$ splitscompletely. Let $\overline{r}:G_F \rightarrow\mathrm{GSp}_4(\overline{\mathbb{F}}_p)$ be a modular Galois representationunramified at all finite places away from $p$ and upper-triangular, maximallynonsplit, and of parallel weight at places dividing $p$. Fix a place $w$dividing $p$. Assuming certain genericity conditions and Taylor--Wilesassumptions, we prove that the $\mathrm{GSp}_4(F_w)$-action on thecorresponding Hecke-isotypic part of the space of mod $p$ automorphic forms ona compact mod center form of $\mathrm{GSp}_4$ with infinite level at $w$determines $\overline{r}|_{G_{F_w}}$.

Mod $p$ local-global compatibility for $\mathrm{GSp}_4(\mathbb{Q}_p)$ in the ordinary case