  We search for an axion-like particle (ALP) $a$ through the process
$\psi(3686)\rightarrow\pi^+\pi^-J/\psi$, $J/\psi\rightarrow\gamma a$,
$a\rightarrow\gamma\gamma$ in a data sample of $(2.71\pm0.01)\times10^9$
$\psi(3686)$ events collected by the BESIII detector. No significant ALP signal
is observed over the expected background, and the upper limits on the branching
fraction of the decay $J/\psi\rightarrow\gamma a$ and the ALP-photon coupling
constant $g_{a\gamma\gamma}$ are set at 95% confidence level in the mass range
of $0.165\leq m_a\leq2.84\,\mbox{GeV}/c^2$. The limits on
$B(J/\psi\rightarrow\gamma a)$ range from $8.3\times10^{-8}$ to
$1.8\times10^{-6}$ over the search region, and the constraints on the
ALP-photon coupling are the most stringent to date for $0.165\leq
m_a\leq1.468\,\mbox{GeV}/c^2$.
