We study the resonant contributions in the process of B¯0→K−π+μ+μ− with the K−π+ invariant mass square mKπ2 involving strange mesons, K⁎(1410),K0⁎(1430),K2⁎(1430),K⁎(1680),K3⁎(1780) and K4⁎(2045). Applying the heavy quark expansion and the large energy limit, we derive the relations of form factors to cancel much of the hadronic uncertainties. Using the dependence of branching fractions on the mKπ, we find that the KJ⁎ resonance has a clear signature. Branching ratios, polarizations, forward–backward asymmetries and transversity amplitudes are predicted, from which we find a promising prospective to observe these channels in the future experiment. We update the constraints on effective Wilson coefficients and/or free parameters in these new physics scenarios by making use of the B→K⁎l+l− and b→sl+l− experimental data. Their impact on B→KJ⁎l+l− is subsequently explored and in particular the zero-crossing point for the forward–backward asymmetry in new physics scenarios can sizably deviate from the standard model.