Panic erupted when the 66 migrants on board the rickety vessel saw a patrol boat from European border agency Frontex approaching, afraid they would be taken back to Turkey, ANA said.
The boy was on the boat with his parents and two younger sisters. When she discovered her son had died in the chaos, his mother tried to end her life by jumping into the sea, only to be rescued by the coastguard.
At least three migrants have drowned this month while attempting to reach Greece, while a nine-year-old girl died in September.
The casualties are far lower than in 2015 and 2016, when hundreds of people drowned, including several children.
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Despite the relative improvement, tragedy continues to strike.
On November 11, the remains of a man, a girl and a boy were found on a Lesbos beach.
According to the unconfirmed reports, the body of the mother and a third child are still missing.