It looks like children ages 5-12 get a strong immune response with 10 micrograms of vaccine antigen, Frenck said.

"So one third of the dose that we're giving adults, or even one third of the dose that was used in 12-year-olds and above, was just as immunogenic. We got just as good an immune response as the 30-microgram dose and there were less side effects," he said.
"So because of that, for the 5-12-year-old dosing we are looking at 10 micrograms, and then, in the younger kids, under 5, even going down further to 3 micrograms."

"We're giving enough vaccine to be able to get the same immune response as we're seeing in people 25 years of age that are getting 30 micrograms."
https://www.cnn.com/2021/08/24/health/covid-19-vaccines-kids-next-wellness/index.html