We study the impact of three different BSM models in the charge asymmetry defined for the 2SS$l$ (with $l= e, \mu$) with jets ($N_{\text{jets}}\geq2$) final state at the LHC, at $\sqrt{s}=13$ TeV, where the main SM contribution is the $t\bar{t}W$ production. We consider the impact of a heavy neutral scalar/pseudoscalar arising from a general two Higgs doublet model (g2HDM); a simplified $R$-parity-violating minimal supersymmetric model (RPV MSSM) with electrowikino production (higgsino or wino-like); and an effective theory with dimension 6 four-quark operators. We propose measuring the charge asymmetries differentially with respect to different kinematic observables, and inclusively/exclusively with the number of b-tagged jets in the final state ($N_b\geq\{1, 2, 3\}$). We show that the 2HDM and the four quark operator scenarios may be sensitive to the detection of new physics, even for an integrated luminosity of 139 fb$^{-1}$.