  Using a data sample of $e^+e^-$ collision data corresponding to an integrated
luminosity of 108 pb$^{-1}$ collected with the BESIII detector at a
center-of-mass energy of 2.125 GeV, we study the process $e^+e^-\rightarrow
\phi\pi\pi$ and search for a strangeoniumlike structure $Z_s$ decaying into
$\phi\pi$. No signal is observed in the $\phi\pi$ mass spectrum. Upper limits
on the cross sections for $Z_s$ production at the 90\% confidence level are
determined. In addition, the cross sections of
$e^+e^-\rightarrow\phi\pi^{+}\pi^{-}$ and $e^+e^-\rightarrow\phi\pi^{0}\pi^{0}$
at 2.125 GeV are measured to be $(436.2\pm6.4\pm30.1)$ pb and
$(237.0\pm8.6\pm15.4)$ pb, respectively, where the first uncertainties are
statistical and the second systematic.
