The most recent data on differential cross sections and photon beam asymmetries \(\Sigma\) from the LEPS2/BGOegg Collaboration for the \(\gamma p \to f_0(980) p\) reaction are analyzed within a tree-level effective Lagrangian approach. The \(t\)-channel \(\rho\) and \(\omega\) exchanges, the \(u\)- and \(s\)-channel \(N\) exchanges, the interaction current, and the possible \(s\)-channel \(N^*\) exchanges are taken into account in constructing the reaction amplitudes to reproduce the data. The results show that the contributions from either the \(N(2040)3/2^+\) or the \(N(2100)1/2^+\) resonance exchange in the \(s\) channel are necessarily required to describe the LEPS2/BGOegg data and they dominate the differential cross sections of \(\gamma p \to f_0(980) p\). Further analysis shows that the contributions from the \(t\)-channel \(\rho\) and \(\omega\) exchanges and the interaction current are rather small to both differential cross sections and photo beam asymmetries, and the contributions from \(u\)-channel \(N\) exchange are considerable in the case of including \(N(2040)3/2^+\) in the model while negligible in the case of including \(N(2100)1/2^+\) in the model. Predictions of target asymmetries \(T\) for \(\gamma p \to f_0(980) p\) are given, which can be examined by future experiments.