  Motivated by the long-standing tension in the muon anomalous magnetic moment
(AMM) and persistent observations of B-physics anomalies in $R_{D^{(\ast)}}$
and $R_{K^{(\ast)}}$ ratios, we construct a simple two-loop radiative neutrino
mass model, and propose a combined explanations of all these apparently
disjoint phenomena within this framework. Our proposed model consists of two
scalar leptoquarks (LQs), a $SU(2)_L$ singlet $S_1\sim (\overline{3},1,1/3)$
and a $SU(2)_L$ triplet $S_3\sim (\overline{3},3,1/3)$ to accommodate
$R_{D^{(\ast)}}$ and $R_{K^{(\ast)}}$ anomalies, respectively. The muon
receives chirality-enhanced contribution towards its $g-2$ due to the presence
of $S_1$ LQ that accounts for the observed deviation from the Standard Model
prediction. Furthermore, we introduce a $SU(2)_L$ singlet scalar diquark
$\omega\sim (\overline{6},1,2/3)$, which is necessary to break lepton number
and generate neutrino mass radiatively with the aid of $S_1$ and $S_3$ LQs. We
perform a detailed phenomenological analysis of this set-up and demonstrate its
viability by providing benchmark points where a fit to the neutrino oscillation
data together with proper explanations of the muon AMM puzzle and flavor
anomalies are accomplished while simultaneously meeting all other flavor
violation and collider bounds.
