Using $1.06 imes10^8$ $psi(3686)$ events recorded in $e^{+}e^{-}$
collisions at $sqrt{s}=$ 3.686 GeV with the BESIII at the BEPCII collider, we
present searches for C-parity violation in $J/psi o gammagamma$ and $
gamma phi$ decays via $psi(3686) o J/psi pi^+pi^-$. No significant
signals are observed in either channel. Upper limits on the branching fractions
are set to be $mathcal{B}(J/psi o gammagamma) < 2.7 imes 10^{-7}$ and
$mathcal{B}(J/psi o gammaphi) < 1.4 imes 10^{-6}$ at the 90\%
confidence level. The former is one order of magnitude more stringent than the
previous upper limit, and the latter represents the first limit on this decay
channel.
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