We report a measurement of the cross section for KS0 pair production in single-tag two-photon collisions, γ∗γ→KS0KS0, for Q2 up to 30 GeV2, where Q2 is the negative of the invariant mass squared of the tagged photon. The measurement covers the kinematic range 1.0 GeV<W<2.6 GeV and |cosθ∗|<1.0 for the total energy and kaon scattering angle, respectively, in the γ∗γ center-of-mass system. These results are based on a data sample of 759 fb-1 collected with the Belle detector at the KEKB asymmetric-energy e+e- collider. For the first time, the transition form factor of the f2′(1525) meson is measured separately for the helicity-0, -1, and -2 components and also compared with theoretical calculations. We have derived the cross section for the process for W<2.6 GeV from 121 signal candidate events. Finally, the γ∗γ partial decay widths of the χc0 and χc2 mesons are measured as a function of Q2 based on 10 candidate events in total.