In this work, a comprehensive analysis for processes related to $b\to c\bar{u}q(q=d,s)$ transitions are carried out, including new physics contributions. In light of a recent tension between branching fractions for $B_{(s)}\to D_{(s)}^{(*)}M$ ($M=\pi ,K$) decays in the QCD factorization approach and relevant experimental results, phenomenological constraints on complex-valued Wilson coeffients are discussed. Analyzed observables contain direct CP asymmetry ($A_{\mathrm{\text{CP}}}$) in $B^{-}\to D^0{\pi }^{-}$ decays and $\gamma /{\varphi }_3$, one of the angles in the unitarity triangle, combined with others from ${\tau }_{B^{+}}/{\tau }_{B_d}$, $\Delta {\Gamma }_q/{\Gamma }_q$, and $A_{\rm SL}^{q}~(q=d, s)$. We constrain the complex Wilson coefficients at $1\sigma$ and $2\sigma$ levels under color-singlet and color-rearranged scenarios. These constraints yield correlated predictions for $\Delta {\Gamma }_d/{\Gamma }_d$, $A_{\rm SL}^d$ and $A_{\mathrm{\text{CP}}}$.