  We investigate the photon-axionlike particle (ALP) oscillation effects on TeV
gamma-ray spectral irregularities from the uncertain redshift active galactic
nuclei (AGN) VER J0521+211. The gamma-ray spectra are measured by Fermi-LAT and
VERITAS with the three flux states in 2013 and 2014. We set the combined
constraints on the ALP parameter ($m_a, g_{a\gamma}$) space with these states
and test the extragalactic background light (EBL) absorption effect on ALP
constraints with the redshift limit scenarios $z_0\sim\mathcal{O}(0.1-0.3)$.
The 99% $\rm C.L.$ photon-ALP combined constraints set by VER J0521+211 are
roughly at $g_{a\gamma} \gtrsim 2.0\times 10^{-11} \rm \, GeV^{-1}$ for
$1.0\times10^{-9} \, {\rm eV} \lesssim m_a \lesssim 1.0\times10^{-7} \, {\rm
eV}$. We find no clear connection between the redshift limit scenarios and the
photon-ALP constraints. Both the underestimated and overestimated redshifts can
affect the constraint results.
