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Abstract The strange quark content of the proton is probed through the measurement of the production cross section for a W boson and a charm (c) quark in proton–proton collisions at a center-of-mass energy of 13$$\,\text {Te}\hspace{-.08em}\text {V}$$ $\text{Te}\text{V}$. The analysis uses a data sample corresponding to a total integrated luminosity of 138$$\,\text {fb}^{-1}$$ ${\text{fb}}^{-1}$collected with the CMS detector at the LHC. The W bosons are identified through their leptonic decays to an electron or a muon, and a neutrino. Charm jets are tagged using the presence of a muon or a secondary vertex inside the jet. The$$\hbox {W}+\hbox {c}$$ $\text{W}+\text{c}$production cross section and the cross section ratio$$R_\textrm{c}^{\pm }= \sigma ({\hbox {W}}^{+}+\bar{\text {c}})/\sigma (\hbox {W}^{-}+{\textrm{c}})$$ $R_{\text{c}}^{\pm }=\sigma ({\text{W}}^{+}+\overline{\text{c}})/\sigma ({\text{W}}^{-}+\text{c})$are measured inclusively and differentially as functions of the transverse momentum and the pseudorapidity of the lepton originating from the W boson decay. The precision of the measurements is improved with respect to previous studies, reaching 1% in$$R_\textrm{c}^{\pm }= 0.950 \pm 0.005\,\text {(stat)} \pm 0.010 \,\text {(syst)} $$ $R_{\text{c}}^{\pm }=0.950\pm 0.005\text{(stat)}\pm 0.010\text{(syst)}$. The measurements are compared with theoretical predictions up to next-to-next-to-leading order in perturbative quantum chromodynamics.