  At the beginning of 2020, MAGIC reported a very-high-energy (VHE) flaring
activity from the FSRQ QSO B1420+326. It is now the fourth known most distant
blazar (z=0.682) with an observed VHE gamma-ray emission. In this work, we
investigate the effect of photon-axionlike particle (ALP) oscillations in the
gamma-ray spectra measured by Fermi-LAT and MAGIC around the flaring state. We
set 95% C.L. upper limit on the ALP parameters and obtain a constraint on the
photon-ALP coupling constant $g_{a\gamma} < 2\times10^{-11}$ GeV$^{-1}$ for ALP
masses $m_{a} \sim 10^{-10}-10^{-9}$ eV. Assuming the hadronic origin of VHE
photons, we also estimate the expected neutrino flux from this source and the
contribution to diffuse neutrino flux from QSO B1420+326-like FSRQs at sub-PeV
energies. Furthermore, we study the implications of photon-ALP oscillations on
the counterpart $\gamma$-rays of the sub-PeV neutrinos. Finally, we investigate
a viable scenario of invisible neutrino decay to ALPs on the gamma-ray spectra
and diffuse $\gamma$-ray flux at sub-PeV energies. Interestingly, we find that
for the choice of neutrino lifetime $\tau_{2}/m_{2} = 10^3$ s eV$^{-1}$, the
$\gamma$-ray flux has a good observational sensitivity towards LHAASO-KM2A.
