An “underage” boy (i.e. not yet bar mitzvah) can spin tzitzit strings or tie tzitzit onto a tallit for himself, but not for an adult.
Tying Tzitzit for an Adult
In order to make or tie tzitzit knots for an adult, he must have entered his 14th year (i.e. 13 and one day) and show signs of physical maturity (shtei sayerot).
The above applies as a general rule in various situations: someone who is not obligated to fulfill the mitzvah cannot perform it for someone who is obligated. For example, a child cannot recite Kiddush for an adult or bake Seder Night matzahs for an adult.
Under some circumstances a child would be allowed to make or tie tzitzit knots for an adult, provided the adult teaches him to do it properly and supervises the work.
Bar Mitzvah Tzitzit: Can He Do the Job Himself?
But what if a young man wants to tie tzitzit on his own tallit before his bar mitzvah? Once he reaches maturity to perform mitzvahs (i.e. 13 and one day), can he now rely on his “boyhood” self? According to the Bei’ur Halacha he can rely on his “old self,” provided he tied them with the mitzvah of tzitzit in mind (O.C. 14 s.v. lehatzrich anashim).
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