We have analyzed the $\gamma p\rightarrow p\pi^0\eta$ process with a particular focus on the role of a triangle singularity which appears in the decay of the $\Delta(1700)$ into $\eta\Delta(1232)$, where the $\Delta(1232)$ goes into $p$ emitting a $\pi^0$, while the $N(1535)$ is formed from the $\eta p$ interaction.
In addition, the tree-level contribution stemming from the $\gamma p\rightarrow \Delta(1700)\rightarrow\eta\Delta(1232)$ process followed by $\Delta(1232)\rightarrow\pi^0 p$ is taken into account.
We have obtained a characteristic energy dependence from the triangle diagram in the $\pi^0N(1535)$ production, and a good agreement with the experimental determination up to $1.3$ GeV.