  We report hole and electron doping in La-doped YBa$_2$Cu$_3$O$_y$(YBCO) thin
films synthesized by pulsed laser deposition technique and subsequent
\emph{in-situ} postannealing in oxygen ambient and vaccum. The $n$-type samples
show a metallic behavior below the Mott limit and a high carrier density of
$\sim2.8$ $\times$ 10$^{21}$ cm$^{-3}$ at room temperature (\emph{T}) at the
optimally reduced condition. The in-plane resistivity ($\rho$$_{ab}$) of the
$n$-type samples exhibits a quadratic \emph{T} dependence in the
moderate-\emph{T} range and shows an anomaly at a relatively higher \emph{T}
probably related to pseudogap formation analogous to underdoped
Nd$_{2-x}$Ce$_x$CuO$_4$ (NCCO). Furthermore, $\rho$$_{ab}$(T), \emph{T}$_c$ and
\emph{T} with minimum resistivity (\emph{T}$_{min}$) were investigated in both
$p$- and $n$-side. The present results reveal the $n$-$p$ asymmetry (symmetry)
within the metallic-state region in an underdoped cuprate and suggest the
potential toward ambipolar superconductivity in a single YBCO system.
