  New vectorlike quarks are predicted in many new physics scenarios beyond the
Standard Model~(SM) and could potentially be discovered at the LHC. Based on a
simplified model including a singlet vectorlike top partner with charge $2/3$,
we investigate the process $pp \to TT$ via a $t$-channel induced by the
couplings between the top partner with the first-generation SM quarks. We
calculate the production cross section and further study the observability of
the heavy top partner in the channel $T\to Wq$ at the high-luminosity LHC
(HL-LHC) using final states with same-sign dileptons (electrons or muons), two
jets, and missing transverse momentum. At the 14 TeV LHC with an integrated
luminosity of 3000 fb$^{-1}$, the $2\sigma$ exclusion limits, as well as the
$5\sigma$ discovery reach in the parameter plane of the two variables
$g^{\ast}-R_L$, are respectively obtained at the HL-LHC. We also obtain the
$2\sigma$ exclusion limit on the coupling strength parameter $g^{\ast}$ in the
case in which the vectorlike top partner is coupled only to the
first-generation quarks.
