Flavored Peccei-Quinn symmetries in the minimal $\nu$DFSZ model

We consider a Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) axion model extended with two right-handed neutrino fields to realize the minimal type-I seesaw. In this $\nu$DFSZ scheme we systematically determine the simplest quark and lepton flavor patterns compatible with masses, mixing and charge-parity violation data, realized by flavored U(1) Peccei-Quinn (PQ) symmetries. We discuss axion dark matter production in pre and post-inflationary cosmology in this context, and predictions for the axion couplings to photons and fermions. In particular, helioscopes and haloscopes are able to probe our models via their distinct axion-to-photon couplings, while in the quark sector the most stringent constraints on axion-fermion couplings are set by $K^+ \rightarrow \pi^+ + a$. Flavor-violating constraints in the lepton sector are not as relevant as those stemming from star cooling that restrict the diagonal $ee$ and $\mu\mu$ axion couplings to charged leptons. We also obtain axion mass bounds for the most interesting models and discuss how minimal flavored PQ symmetries provide a natural framework to suppress flavor-violating couplings.