In this work, the gamma prightarrow phi (1680) p reaction is systematically studied based on the two gluon exchange model and the pomeron model. The calculation results show that the total cross section of phi (1680) photoproduction can reach more than 80 nb near the center-of-mass energy W=4 GeV, so it is suggested that JLab and other experiments carry out relevant measurements. Moreover, under the framework of the vector meson dominance assumption, the scattering length of phi (1680) and proton interaction is estimated as 0.07pm 0.01 fm from the cross sections predicted by the theoretical models, which is on the same order of magnitude as the phi (1020)-p scattering length. In addition, the total cross section, number of events and rapidity distribution of phi (1680) production are predicted at Electron-Ion colliders (EICs) and ultra-peripheral collisions (UPCs) by using eSTARlight and STARlight code. The study of phi (1680) and relevant properties is of enlightening significance in better understanding the strangeonium family spectrum, and provides necessary data support for the future experiment of EICs and UPCs.