Halacha Orach Chaim 225
The Rama writes that when a child reaches the Age of thirteen, his father should recite the Bracha of Baruch Sheptarani Mayonsho Shell Zeh. This Bracha is recited without the Shem.
The reason for this Bracha is because a father is responsible for the sins of his child until the child reaches the age of thirteen, as he should have taught him to refrain from sin. From the age of thirteen he is less responsible. Although, the Chofetz Chaim makes a point of mentioning the dictum of Chazal that one who does not rebuke an older child is considered responsible for his sins, and one who does not rebuke members of a community will be held responsible for their sins as well. Obviously a Halachic authority should be consulted how this should be done.
The Levush brings the exact opposite reasoning for this Bracha. Until a child is thirteen, he is punished on account of the father’s shortcomings. From the age of thirteen, the child does not directly suffer from his father’s inequities.
The Chofetz Chaim writes that the accepted custom is to only recite this Bracha at the time the Bar Mitzva boy is participating like other adults in a Minyan. He can do this, according to the Chofetz Chaim, either by reading the Torah or representing the Minyan as the Chazon. The reason for this is because at that time he becomes known to all as a full fledged responsible member of Klal Yisroel. The accepted custom is to recite this Bracha after an Aliyah to the Torah. Ketzos Hashulchan writes that there is no limit as to when this Bracha can be recited, if delayed.
The Mishna Berura brings the Magen Avrohom that recommends one to make a Seudah on the day a child becomes obligated in Mitzvos. The Chofetz Chaim adds that if the Bar Mitzva boy says over words of Torah, the Seuda becomes a Seudas Mitzva, even if it was delayed. In addition, the Chaye Adam writes that if the child says words of Torah, meat can be eaten during the nine days, as it has the status of a Seudas Mitzva.