  We investigate the single production of vector-like quarks at the High
Luminosity LHC (HL-LHC). With the assumed (enhanced) couplings to third
generation quarks of the standard model, vector-like quarks $B/X$ are produced
in association with a bottom ($b$) or top ($t$) quark, which correspond to
$Bbq$ and $Btq/Xtq$ production modes, including an additional soft forward jet
from the spectator quark ($q$). This study focuses on high-mass vector-like
quarks $B/X$ decaying into a top quark and a $W$ boson, resulting in the final
state jets emerging from hadronically decaying top quark ($t\to Wb$) and $W$
boson ($W\to q\bar{q}'$). The events with $W$ boson and $t$ quark have been
analysed using tagging techniques for large-radius jets. The scan ranges of the
mass ($1000<m_{B/X}<3000$ GeV) for the relative width
$\Gamma_{B/X}/m_{B/X}=0.1$ and $\Gamma_{B/X}/m_{B/X}=0.01$ of vector-like $B/X$
quarks have been investigated. From the results of the analysis, the masses of
vector like quarks $B$($X$) up to $2491$ ($2364$) GeV and $2018$ ($1873$) GeV
can be excluded corresponding to these relative width cases at $95\%$ CL
depending on the type and branching scenarios at integrated luminosity
projection of $3$ ab$^{-1}$ at the HL-LHC.
