Thirteen Years And A Day
The Mishnah Berurah writes (225:6), “There is a mitzvah for an individual to make a festive meal on the day when his son becomes bar mitzvah like the day that he marries. . . .
Chinuch
Exact Time a Boy Becomes Bar Mitzvah in the Gemara
Whether a boy becomes bar mitzvah at the start of his thirteenth birthday or only at the hour he was born, and what thirteen years and a day means.