The reactions γp→ηp and γp→η^{'}p are measured from their thresholds up to the center-of-mass energy W=1.96 GeV with the tagged-photon facilities at the Mainz Microtron, MAMI. Differential cross sections are obtained with unprecedented statistical accuracy, providing fine energy binning and full production-angle coverage. A strong cusp is observed in the total cross section for η photoproduction at the energies in the vicinity of the η^{'} threshold, W=1896 MeV (E_{γ}=1447 MeV). Within the framework of a revised ηMAID isobar model, the cusp, in connection with a steep rise of the η^{'} total cross section from its threshold, can only be explained by a strong coupling of the poorly known N(1895)1/2^{-} state to both ηp and η^{'}p. Including the new high-accuracy results in the ηMAID fit to available η and η^{'} photoproduction data allows the determination of the N(1895)1/2^{-} properties.