We analyze 13.8 \rm fb^{-1} of the integrated e^+e^- luminosity collected at
10.6 GeV center-of-mass energy with the CLEO II and CLEO II.V detectors to
study exclusive two-photon production of hadrons with masses below 1.7{\rm \
GeV/c^2} decaying into the K^0_S K^\pm \pi^\mp final state. We observe two
statistically significant enhancements in the \eta(1440) mass region. These
enhancements have large transverse momentum which rules them out as being due
to pseudoscalar resonances but is consistent with the production of
axial-vector mesons. We use tagged two-photon events to study the properties of
the observed enhancements and associate them with the production of f_1(1285)
and f_1(1420). Our non-observation of \eta(1440) is inconsistent by more than
two standard deviations with the first observation of this resonance in
two-photon collisions by the L3 experiment. We present our estimates for 90%
confidence level upper limits on the products of two-photon partial widths of
pseudoscalar hadrons and their branching fractions into
K^0_S(\pi^+\pi^-)K^\pm\pi^\mp.Comment: 24 pages postscript,also available through
http://www.lns.cornell.edu/public/CLNS/2004/, submitted to PR