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We study ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{h}_{c}$ at center-of-mass energies from 3.90 to 4.42 GeV by using data samples collected with the BESIII detector operating at the Beijing Electron Positron Collider. The Born cross sections are measured at 13 energies and are found to be of the same order of magnitude as those of ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}J/\ensuremath{\psi}$ but with a different line shape. In the ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}{h}_{c}$ mass spectrum, a distinct structure, referred to as ${Z}_{c}(4020)$, is observed at $4.02\text{ }\text{ }\mathrm{GeV}/{c}^{2}$. The ${Z}_{c}(4020)$ carries an electric charge and couples to charmonium. A fit to the ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}{h}_{c}$ invariant mass spectrum, neglecting possible interferences, results in a mass of $(4022.9\ifmmode\pm\else\textpm\fi{}0.8\ifmmode\pm\else\textpm\fi{}2.7)\text{ }\text{ }\mathrm{MeV}/{c}^{2}$ and a width of $(7.9\ifmmode\pm\else\textpm\fi{}2.7\ifmmode\pm\else\textpm\fi{}2.6)\text{ }\text{ }\mathrm{MeV}$ for the ${Z}_{c}(4020)$, where the first errors are statistical and the second systematic. The difference between the parameters of this structure and the ${Z}_{c}(4025)$ observed in the ${D}^{*}{\overline{D}}^{*}$ final state is within $1.5\ensuremath{\sigma}$, but whether they are the same state needs further investigation. No significant ${Z}_{c}(3900)$ signal is observed, and upper limits on the ${Z}_{c}(3900)$ production cross sections in ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}{h}_{c}$ at center-of-mass energies of 4.23 and 4.26 GeV are set.

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