  Since the definition of $T\bar{T}$ deformation in the curved Riemann surface
is obstructive in the literature, we propose a way to do the deformation in the
genus two Riemann surfaces by sewing prescription. We construct the correlation
functions of conformal field theories (CFTs) on genus two Riemann surfaces with
the $T\bar{T}$ deformation in terms of the perturbative CFT approach. Thanks to
sewing construction to form higher genus Riemann surfaces from lower genus ones
and conformal symmetry, we systematically obtain the first order $T\bar{T}$
correction to the genus two correlation functions in the $T\bar{T}$ deformed
CFTs, e.g., partition function and one/higher-point correlation functions.
