  We present a study of the process $e^+e^-\to\pi^{\pm}(D\bar{D}^*)^{\mp}$
using data samples of 1092~pb$^{-1}$ at $\sqrt{s}=4.23$~GeV and 826~pb$^{-1}$
at $\sqrt{s}=4.26$~GeV collected with the BESIII detector at the BEPCII storage
ring. With full reconstruction of the $D$ meson pair and the bachelor
$\pi^{\pm}$ in the final state, we confirm the existence of the charged
structure $Z_c(3885)^{\mp}$ in the $(D\bar{D}^*)^{\mp}$ system in the two
isospin processes $e^+e^-\to\pi^+D^0D^{*-}$ and $e^+e^-\to\pi^+D^-D^{*0}$. By
performing a simultaneous fit, the statistical significance of $Zc(3885)^{\mp}$
signal is determined to be greater than 10$\sigma$, and its pole mass and width
are measured to be
$M_{\rm{pole}}$=(3881.7$\pm$1.6(stat.)$\pm$1.6(syst.))~MeV/$c^2$ and
$\Gamma_{\rm{pole}}$=(26.6$\pm$2.0(stat.)$\pm$2.1(syst.))~MeV, respectively.
The Born cross section times the $(D\bar{D}^*)^{\mp}$ branching fraction
($\sigma(e^+e^-\to\pi^{\pm}Z_{c}(3885)^{\mp}) \times
Br(Z_{c}(3885)^{\mp}\to(D\bar{D}^*)^{\mp})$) is measured to be
$(141.6\pm7.9(\text{stat.})\pm12.3(\text{syst.}))~\text{pb}$ at
$\sqrt{s}=4.23$~GeV and
$(108.4\pm6.9(\text{stat.})\pm8.8(\text{syst.}))~\text{pb}$ at
$\sqrt{s}=4.26$~GeV. The polar angular distribution of the
$\pi^{\pm}$-$Z_c(3885)^{\mp}$ system is consistent with the expectation of a
quantum number assignment of $J^P=1^+$ for $Z_c(3885)^{\mp}$.
