  3HSP J095507.9+355101 is an extreme blazar which has been possibly associated
with a high-energy neutrino (IceCube-200107A) detected one day before the
blazar was found to undergo a hard X-ray flare. We perform a comprehensive
study of the predicted multimessenger emission from 3HSP J095507.9+355101
during its recent X-ray flare, but also in the long term. We focus on one-zone
leptohadronic models, but we also explore alternative scenarios: (i) a
blazar-core model, which considers neutrino production in the inner jet, close
to the supermassive black hole; (ii) a hidden external-photon model, which
considers neutrino production in the jet through interactions with photons from
a weak broad line region; (iii) a proton synchrotron model, where high-energy
protons in the jet produce $\gamma$-rays via synchrotron; and (iv) an
intergalactic cascade scenario, where neutrinos are produced in the
intergalactic medium by interactions of a high-energy cosmic-ray beam escaping
the jet. The Poisson probability to detect one muon neutrino in ten years from
3HSP J095507.9+355101 with the real-time IceCube alert analysis is $\sim 1\%$
($3\%$) for the most optimistic one-zone leptohadronic model (the multi-zone
blazar-core model). Meanwhile, detection of one neutrino during the 44-day-long
high X-ray flux-state period following the neutrino detection is $0.06\%$,
according to our most optimistic leptohadronic model. The most promising
scenarios for neutrino production also predict strong intra-source $\gamma$-ray
attenuation above $\sim100$ GeV. If the association is real, then IceCube-Gen2
and other future detectors should be able to provide additional evidence for
neutrino production in 3HSP J095507.9+355101 and other extreme blazars.
