  We consider production of overall neutral pairs consisting of heavy $D^{(*)}$
or $B^{(*)}$ meson and antimeson in the processes, where the pair can be
created in an $S$-wave, such as $e^+e^- \to \pi^0 \, D^* \bar D^{(*)}$ and
$e^+e^- \to \gamma \, D^{(*)} \bar D^{(*)}$, and similar reactions with
$B^{(*)}$ mesons. The ratio $R^{c/n}$ of the yield of pairs of charged mesons
to that of neutral mesons near the threshold for the heavy pair is strongly
affected by the isospin breaking due to the isotopic mass differences and due
to the Coulomb interaction between the charged mesons. The actual behavior of
the isospin breaking in $R^{c/n}$ is also sensitive to the strong interaction
between the heavy mesons, so that experimental measurement of this ratio can be
used as a probe of this strong interaction. We calculate $R^{c/n}$ at and very
near the threshold in terms of the isotopic scattering lengths for the meson
pairs. In particular we find that the yield of pairs of charged mesons does not
go to zero at exactly the threshold, but rather starts with a finite step,
whose height depends on the value of the scattering length in a particular
channel.
