When R. Baruch entered the Baal Shem Tov's study ... he told the tzaddik that he and his wife had decided to bring their son with them for the following year's Chai Elul. The [three-year-old] child would then have his first haircut and would be left with peyos. The Baal Shem Tov agreed, told the father to keep his child out of sight, and to see to it that he should be accompanied by his mother and by his aunt Devorah Leah. They were to arrive after morning prayers on Chai Elul, and as soon as he himself had cut the child's hair in his study they were to leave incognito.
... On Wednesday, Chai Elul, 5508 (1748), Rebbitzin Rivkah and her sister-in-law duly arrived in Mezhibuzh. As soon as the Baal Shem Tov had given the child his first training in leaving his peyos uncut, and had given him his blessing, he urged them to leave immediately and not to discuss between themselves where they had been. Finally, he wished them a good year and a safe journey home.
The little boy kept on asking who was this man who had cut his hair and left him with peyos, and who had blessed him.
"That was a grandfather," replied his mother.
(Likkutei Dibburim, Vol. III, p. 247)
On Erev Rosh HaShanah, 5553, [my great-]grandfather, [the Tzemach Tzedek,] became three years old.... After the [morning] prayers, [my great-]grandfather was given his first hair-cut, and peyos were left. The [Alter] Rebbe blessed him, placing his holy hands on his holy head.
(Sefer HaSichos Kayitz 5700, p. 40)
When [the Rebbe Rashab] was three years old, [the Tzemach Tzedek] ordered that [the ceremony at which] his hair would be cut and his peyos left should be carried out secretly. In the evening, before the beginning of the day when the youth would become three, he ordered that the youth should be brought to [the Tzemach Tzedek's] room and that he should spend the night there.
In the morning, when [the child] awoke, [the Tzemach Tzedek] instructed the attendant Reb Chayim Ber that [the child] should wash his hands by himself. He said the [morning] blessings with him and responded Amen.
After the [morning] prayers, he called the child's parents, my revered grandfather and teacher, [the Rebbe Maharash,] and my grandmother, and told them: "Our master, the Baal Shem Tov, gave a spiritual cruse of oil to his disciple, the Maggid of Mezeritch, to anoint the Alter Rebbe and grant him leadership for the coming generations. With this power, my father-in-law, the Mitteler Rebbe was anointed. With this power, I anointed you, and with this power, I am anointing him.
(Sefer HaMaamarim 5710, p. 163.)
When as a child, they brought me (the Previous Rebbe) to the cheder for the first time, my father and my uncle, Raza, were there. As is customary, they threw candies at me, and they told me that the angel Michael threw them.
My father told me that when he began going to Cheder, it was [still] in the lifetime of the Tzemach Tzedek. They threw candies at him and told him that it was the Angel Michoel who threw them. He believed them and therefore did not want to eat the candies, because he considered them very precious.
On the day before Pesach, when it was customary to check the pockets of the small children, the Tzemach Tzedek called my father and asked him where the candies were. Then he had to eat them.
(Sefer HaSichos 5701, pp.29-30)
After the [morning] prayers, the Alter Rebbe ordered that we should wrap the child in a tallis so that he could not see anything and carry him by hand to his mother's grave. The Rebbe, all the members of his household, all the members of the family who were in Liozna, and many chassidim went to the holy place (the cemetery).
The Alter Rebbe approached the grave and announced in a cheerful voice: "Mazel Tov, Devorah, the daughter of Shterna. Today, I am bringing your son, Menachem Mendel, the son of Devorah Leah to Torah study. Bless him that just as he enters the study of the Torah, he should proceed to marriage and good deeds."
All the assembled cried out: Amen.
After returning from the cemetery, the Rebbe said that the child should be taken to the synagogue.... The Rebbe told [the teacher] to teach the child the first passage in Vayikra. The Rebbe [sat] in d'veikus, his head resting on his holy arms.
[The teacher] taught the child the passage. The Rebbe gave the child a honey-cookie cooked in oil and a hard-boiled egg. In the dough of the cookie were inscribed certain verses. Similarly, there were verses written on the egg.
(Sefer HaSichos Kayitz 5700, p. 67-68)