We suggest that the exclusive Higgs þ light (or b)-jet production at the LHC, pp → h þ jðj b Þ, is a rather sensitive probe of the light-quarks Yukawa couplings and of other forms of new physics (NP) in the Higgs-gluon hgg and quark-gluon qqg interactions. We study the Higgs, in h þ jðj b Þ production followed by the Higgs decay h → γγ, employing the (p T -dependent) signal strength formalism to probe various types of NP which are relevant to these processes and which we parametrize either as scaled Standard Model (SM) couplings (the kappaframework) and/or through new higher dimensional effective operators (the SMEFT framework). We find that the exclusive h þ jðj b Þ production at the 13 TeV LHC is sensitive to various NP scenarios, with typical scales ranging from a few TeV to Oð10Þ TeV, depending on the flavor, chirality and Lorentz structure of the underlying physics.