Abstract In 2019 July, the IceCube experiment detected a high-energy neutrino from the direction of the powerful blazar PKS 1502+106. We perform multiwavelength and multimessenger modeling of this source, using a fully selfconsistent one-zone model that includes the contribution of external radiation fields typical of flat-spectrum radio quasars. We identify three different activity states of the blazar: one quiescent state and two flaring states with hard and soft gamma-ray spectra. We find two hadronic models that can describe the multiwavelength emission during all three states: a leptohadronic model with a contribution from photohadronic processes to X-rays and gamma-rays, and a proton synchrotron model, where the emission from keV to 10 GeV comes from proton synchrotron radiation. Both models predict a substantial neutrino flux that is correlated with the gamma-ray and soft X-ray fluxes. Our results are compatible with the detection of a neutrino during the quiescent state, based on event rate statistics. We conclude that the soft X-ray spectra observed during bright flares strongly suggest a hadronic contribution, which can be interpreted as additional evidence for cosmic-ray acceleration in the source independently of neutrino observations. We find that more arguments can be made in favor of the leptohadronic model vis-a-vis the proton synchrotron scenario, such as a lower energetic demand during the quiescent state. However, the same leptohadronic model would be disfavored for flaring states of PKS 1502+106 if no IceCube events were found from the direction of the source before 2010, which would require an archival search.