Date: Tzom Gedaliah 5575
From: Rabbi Moshe Sofer
To: Rabbi Naftali
A boy whose thirteenth birthday falls on Yom Kippur — is he obligated in the fast and in tosefes? The Chasam Sofer rules he must fast from the onset of Yom Kippur itself but is exempt from tosefes, since 'there is no tosefes without an existing base obligation.'
Source: Shu"t Chasam Sofer OC §172