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.
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