To purchase this Sefer, click here
It is proper to cover even the head of children [in order to place upon them fear of heaven].
From what age should a child begin to wear a Yarmulke?
Age three: From age three we are particular that a boy does not walk without a Yarmulke.
Before age three: Many have the custom to place a Yarmulke on their child even before age three, and some even do so as soon as the child is born. However the custom of the world is not to be particular about this.
Are children to wear a Yarmulke during sleep?
Yes. Children are to wear a Yarmulke even when sleeping.
A Maaseh Shehaya:
There were once two children who walked pass the elders of the city which were sitting by the city gate. One child had a head covering on him while the other did not. The elders began discussing the lineage of the child who did not cover his head. Rebbi Elazar said that the child is a bastard. Rebbi Y. said that he was conceived when his mother was a Niddah. Rebbi Akiva said that he is both a bastard and the child of a Niddah. At that time they said “Blessed be G-d the G-d of Israel for revealing his secrets to Rebbe Akiva the son of Yosef”.
 Kama 2/7; Basra 2/6; based on M”A 2/6 and Tractate Shabbos 156; So also rules: Elya Raba 2/4; Kitzur SH”A 3/6; M”B 2/11
The Gemara in Shabbos ibid states that the mother of Rebbe Nachman Bar Yitzchak was careful to cover his head even when he was a small child.
 Kama ibid
 Shaareiy Halacha Uminhag 2 p. 300
 Igros Kodesh 9 p. 181; Shaareiy Halacha Uminhag ibid; Shulchan Hatahor Tznius 5; Divrei Yatziv 91; Shraga Hameir 3/80; See also Mishneh Halachos 7/2
 The will of the Rebbe Rashab to the general public printed in Ishkavta Dirrebe p. 136
 Divrei Yatziv ibid; Piskeiy Teshuvos 2/11
 Igros Kodesh 3 p. 397 [brought in Shaareiy Chinuch p. 148]; Shulchan Hatahor Tznius 5
 This story is brought in Tractate Kallah and shows the importance for even children to wear head coverings. [brought in Ketzos Hashulchan 3 footnote 8]