We study the reasonable requirements of two anomalous $U(1)$s in a flavored-axion framework for the anomaly cancellations of both $U(1)$-mixed gravity and $U(1)_Ytimes[U(1)]^2$ which in turn determine the $U(1)_Y$ charges where $U(1)_Y$ is the hypercharge gauge symmetry of the standard model. We argue that, with a flavor symmetry group, axion-induced topology in symmetry-broken phases plays crucial roles in describing how quarks and leptons are organized at a fundamental level and make deep connections with each other. A unified model, as an example, is then proposed in a simple way to describe a whole spectrum of particles where both flavored-axion interactions with normal matter and the masses and mixings of fermions emerge from the spontaneous breaking of a given symmetry group. Once a scale of active neutrino mass defined at a seesaw scale is fixed by the commensurate $U(1)$ flavored-PQ charge of fermions, that of QCD axion decay constant $F_A$ is determined. In turn, fundamental physical parameters complementary to each other are predicted with the help of precision flavor experiments. Model predictions are extracted on the characteristics of neutrino and flavored-axion: $F_A=3.57^{,+1.52}_{,-1.53}times10^{10}$ GeV (consequently, QCD axion mass $m_a=1.52^{+1.14}_{-0.46}times10^{-4}$ eV, axion to photon coupling $|g_{agammagamma}|=2.15^{+1.61}_{-0.64}times10^{-14},text{GeV}^{-1}$, axion to electron coupling $g_{Aee}=3.29^{+2.47}_{-0.98}times10^{-14}$, etc.); atmospheric mixing angle $theta_{23}$, Dirac CP phase $delta_{CP}$, and $0 ubetabeta${it-decay rate} for normal mass ordering and inverted one by taking quantum corrections into account.
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