  Vectorlike quarks have been predicted in many new physics scenarios beyond
the Standard Model (SM), which can have sizable couplings to first generation
quarks without conflicting with current experimental constraints. In a
framework of the SM simply extended by an SU(2) doublet $\left(X,T\right)$
including a vectorlike quark $X$~(VLQ-$X$), with electric charge $|Q_{X}| =
5/3$, we investigate the single production of the VLQ-$X$ induced by the
couplings between the VLQ-$X$ with the first and the third generation quarks at
the Large Hadron Collider (LHC) Run-III and High-Luminosity LHC (HL-LHC)
operating at $\sqrt{s}=14$~TeV. The signal is searched in events including
same-sign dileptons (electrons or muons), one $b$-tagged jet and missing
energy, where the X quark is assumed to decay into a top quark and a W boson,
both decaying leptonically. After a rapid simulation of signal and background
events, the 95\% CL exclusion limits and the $5\sigma$ discovery reach are
respectively obtained at the 14 TeV LHC with an integrated luminosity of 300
and 3000 fb$^{-1}$, respectively.
