While active galactic nuclei with relativistic jets have long been prime candidates for the origin of extragalactic cosmic rays and neutrinos, the BL Lac object TXS 0506+056  is the first astrophysical source observed to be associated with some confidence (∼3σ) with a high-energy neutrino, IceCube-170922A, detected by the IceCube Observatory. The source was found to be active in high-energy γ-rays with Fermi-LAT and in very-high-energy γ-rays with the MAGIC telescopes. To consistently explain the observed neutrino and multiwavelength electromagnetic emission of TXS 0506+056, we investigate in detail single-zone models of leptohadronic emission, assuming cospatial acceleration of electrons and protons in the jet, and synchrotron photons from the electrons as targets for photohadronic neutrino production. The parameter space concerning the physical conditions of the emission region and particle populations is extensively explored for scenarios where the γ-rays are dominated by either (1) proton synchrotron emission or (2) synchrotron-self-Compton emission, with a subdominant but non-negligible contribution from photohadronic cascades in both cases. We find that the latter can be compatible with the neutrino observations, while the former is strongly disfavoured due to the insufficient neutrino production rate.