A search is conducted for a low-mass charged Higgs boson produced in a top quark decay and subsequently decaying into a charm and an antistrange quark. The data sample was recorded in proton-proton collisions at \sqrt{s}=13~\mathrm{TeV} by the CMS experiment at the LHC and corresponds to an integrated luminosity of 35.9~\mathrm{fb}^{-1}. The signal search is conducted in the process of top-quark pair production, where one top quark decays to a bottom quark and a charged Higgs boson, and the other to a bottom quark and a W boson. With the W boson decaying to a charged lepton (electron or muon) and a neutrino, the final state comprises an isolated lepton, missing transverse momentum, and at least four jets, of which two are tagged as b jets. To enhance the search sensitivity, one of the jets originating from the charged Higgs boson is required to satisfy a charm tagging requirement. No significant excess beyond standard model predictions is found in the dijet invariant mass distribution. An upper limit in the range $0.20$$-$$1.65\%$ is set on the branching fraction of the top quark decay to the charged Higgs boson and bottom quark for a Higgs mass between $80$ and $160$ GeV.

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