  In this work, we perform a study of nucleon resonance production in the
$\gamma p \to p\eta\phi$ reaction within an effective Lagrangian approach. In
our model, we consider the excitation of the $N^*(1535)$, $N^*(1650)$,
$N^*(1710)$ and $N^*(1720)$ in the intermediate state and the background term.
We find that this reaction is dominated by the excitation of the $N^*(1535)$ in
the near threshold region. Especially, we study the possible role of the scalar
meson exchange in this reaction. It is found that the $f_0(980)$ exchange may
give a significant contribution and the parity asymmetry can be used to
identify its role in this reaction.
