The muon ${(g-2)}_{\mu }$ and $b\to s\overline{\mu }\mu$ induced B anomalies as hints of new physics beyond the standard model (SM) have attracted much attention. These two anomalies indicate that there may exist new interaction specifically related to muon. A lot of theoretical ideas have been proposed to explain these anomalies. Gauged flavor specific $U{\left(1\right)}_{B_q-L_{\mu }}$ is among the promising ones. The new gauge boson $Z^{\prime }$ from $U{\left(1\right)}_{B_q-L_{\mu }}$ interacts with muon and provides necessary ingredient to solve the ${(g-2)}_{\mu }$ anomaly. The $Z^{\prime }$-quark coupling can generate flavor changing interactions after diagonalization of quark mass matrix between weak eigen-state and mass eigen-state basis. We revisit challenges for such models attempting to explain the ${(g-2)}_{\mu }$ and B anomalies separately or simultaneously. We find although for $U{\left(1\right)}_{B_q-L_{\mu }}$ models there is still parameter space to provide solutions for separately explaining the ${(g-2)}_{\mu }$ and B anomalies, there exists no parameter space for such models to solve both the anomalies simultaneously, after taking into account existing constraints from $\tau \to \mu \gamma$, $\tau \to 3\mu$, neutrino trident and $B_s-{\overline{B}}_s$ data. Among them leptonic processes restrict $Z^{\prime }$ mass to be less than a few hundred MeV if required to solve the ${(g-2)}_{\mu }$ anomaly, which causes conflict between data from $B_s-{\overline{B}}_s$, $D^0-{\overline{D}}^0$ mixing and also hadron decays with $Z^{\prime }$ in the final states. The effects of $U{\left(1\right)}_Y$ and $U{\left(1\right)}_{B_q-L_{\mu }}$ kinetic mixing on these anomalies are also studied. We find that neither can these effects do much to bring the two anomalies together to be solved simultaneously.