  The origin of the diffuse flux of TeV-PeV astrophysical neutrinos is still
unknown. The $\gamma$-ray blazar PKS 0735+178, located outside the 90\%
localization region at 2.2 deg from the best-fit IC-211208A event, was found to
be flaring across all wavebands. In addition to leptonic synchrotron (SYN) and
synchrotron self-Compton (SSC) emission, we invoke photohadronic ($p\gamma$)
interactions inside the jet to model the spectral energy distribution (SED) and
neutrino emission. We analyze the 100 days $\gamma$-ray and X-ray data and 10
days around the neutrino event is chosen to generate the broadband SED. The
temporal light curve indicates that the source was in a high state in optical,
UV, $\gamma$-ray, and X-ray frequencies during the neutrino detection epoch. In
the one-zone lepto-hadronic model, the SSC photons do not provide enough seed
photons for $p\gamma$ interactions to explain the neutrino event. However,
including an external photon field yields a neutrino event rate of 0.12 in 100
days, for the IceCube detector, using physically motivated values of the
magnetic field, an external photon field peaking at optical wavelength, and
other jet parameters. The radiation from secondary electrons at X-ray energies
severely constrains the neutrino flux to a lower value than found in previous
studies. Moreover, the flux of high-energy $\gamma$-rays at GeV energies from
the decay of neutral pions is subdominant at the high-energy peak of the SED,
suggesting a higher correlation of neutrinos flux with X-ray flux is plausible.
