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Using e+e- collision data collected with the BESIII detector at the BEPCII collider at 32 center-of-mass energies from 3.50 to 4.95 GeV, corresponding to an integrated luminosity of 25 fb-1, we measure the Born cross section of the e+e-→ς0ς¯0 reaction and the effective form factor for the first time. No significant charmonium(-like) state, i.e., ψ(3770), ψ(4040), ψ(4160), ψ(4230), ψ(4360), ψ(4415), or ψ(4660), decaying into the ς0ς¯0 final state is observed by fitting the e+e-→ς0ς¯0 dressed cross section. The upper limits for the product of the branching fraction and the electronic partial width at the 90% confidence level are provided for each assumed charmonium(-like) state for the first time. In addition, the ratios of the Born cross section and the effective form factor between the e+e-→ς0ς¯0 and the e+e-→ς+ς¯- reactions are provided, which can be used to validate the prediction of the vector meson dominance model.