  The left-right twin Higgs model (LRTHM) predicts the existence of the top
partner $T$. In this work, we make a systematic investigation for the single
and pair production of this top partner $T$ through the processes:
$e^{+}e^{-}\to t\ov{T} + T\bar{t}$ and $ T\ov{T}$, the neutral scalar (the
SM-like Higgs boson $h$ or neutral pseudoscalar boson $\phi^{0}$) associate
productions $e^{+}e^{-}\to t\ov{T}h +T\bar{t}h$, $T\ov{T}h$,
$t\ov{T}\phi^{0}+T\bar{t}\phi^{0}$ and $ T\ov{T}\phi^{0}$. From the numerical
evaluations for the production cross sections and relevant phenomenological
analysis we find that (a) the production rates of these processes, in the
reasonable parameter space, can reach the level of several or tens of fb; (b)
for some cases, the peak value of the resonance production cross section can be
enhanced significantly and reaches to the level of pb; (c) the subsequent decay
of $T\to \phi^{+}b \to t\bar{b}b$ may generate typical phenomenological
features rather different from the signals from other new physics models beyond
the standard model(SM); and (d) since the relevant SM background is generally
not large, some signals of the top partner $T$ predicted by the LRTHM may be
detectable in the future ILC and CLIC experiments.
