  The Born cross sections of $e^{+}e^{-}\to \Sigma^{0}\bar{\Sigma}^{0}$ are
measured at center-of-mass energies from $2.3864$ to $3.0200$ GeV using data
samples with an integrated luminosity of $328.5$ pb$^{-1}$ collected with the
BESIII detector operating at the BEPCII collider. The analysis makes use of a
novel reconstruction method for energies near production threshold, while a
single-tag method is employed at other center-of-mass energies. The measured
cross sections are consistent with earlier results from BaBar, with a
substantially improved precision. The cross-section lineshape can be well
described by a perturbative QCD-driven energy function. In addition, the
effective form factors of the $\Sigma^{0}$ baryon are determined. The results
provide precise experimental input for testing various theoretical predictions.
