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We present a study of the process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}(D{\overline{D}}^{*}{)}^{\ensuremath{\mp}}$ using data samples of $1092\text{ }\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$ at $\sqrt{s}=4.23\text{ }\text{ }\mathrm{GeV}$ and $826\text{ }\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$ at $\sqrt{s}=4.26\text{ }\text{ }\mathrm{GeV}$ collected with the BESIII detector at the BEPCII storage ring. With full reconstruction of the $D$ meson pair and the bachelor ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$ in the final state, we confirm the existence of the charged structure ${Z}_{c}(3885{)}^{\ensuremath{\mp}}$ in the $(D{\overline{D}}^{*}{)}^{\ensuremath{\mp}}$ system in the two isospin processes ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{D}^{0}{D}^{*\ensuremath{-}}$ and ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{D}^{\ensuremath{-}}{D}^{*0}$. By performing a simultaneous fit, the statistical significance of $Zc(3885{)}^{\ensuremath{\mp}}$ signal is determined to be greater than $10\ensuremath{\sigma}$, and its pole mass and width are measured to be ${M}_{\mathrm{pole}}=(3881.7\ifmmode\pm\else\textpm\fi{}1.6(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}1.6(\mathrm{syst}))\text{ }\text{ }\mathrm{MeV}/{c}^{2}$ and ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{pole}}=(26.6\ifmmode\pm\else\textpm\fi{}2.0(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}2.1(\mathrm{syst}))\text{ }\text{ }\mathrm{MeV}$, respectively. The Born cross section times the $(D{\overline{D}}^{*}{)}^{\ensuremath{\mp}}$ branching fraction ($\ensuremath{\sigma}({e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}{Z}_{c}(3885{)}^{\ensuremath{\mp}})\ifmmode\times\else\texttimes\fi{}Br({Z}_{c}(3885{)}^{\ensuremath{\mp}}\ensuremath{\rightarrow}\phantom{\rule{0ex}{0ex}}(D{\overline{D}}^{*}{)}^{\ensuremath{\mp}})$) is measured to be $(141.6\ifmmode\pm\else\textpm\fi{}7.9(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}12.3(\mathrm{syst}))\text{ }\text{ }\mathrm{pb}$ at $\sqrt{s}=4.23\text{ }\text{ }\mathrm{GeV}$ and $(108.4\ifmmode\pm\else\textpm\fi{}6.9(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}8.8(\mathrm{syst}))\text{ }\text{ }\mathrm{pb}$ at $\sqrt{s}=4.26\text{ }\text{ }\mathrm{GeV}$. The polar angular distribution of the ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{-}{Z}_{c}(3885{)}^{\ensuremath{\mp}}$ system is consistent with the expectation of a quantum number assignment of ${J}^{P}={1}^{+}$ for ${Z}_{c}(3885{)}^{\ensuremath{\mp}}$.