L’chatchilah, spinning should be done by a Jewish adult man or woman without disqualifying conditions. If this is not possible, a child, deaf-mute or shoteh can also spin the threads if an adult supervises and instructs the person to do it lishmah. A non-Jew can also spin the wool under these conditions if need be. The poskim disagree about whether these supervised sessions would be permissible if they were to extend over a long period of time. Without adult supervision, tzitzis spun in these circumstances are not acceptable.
[סעיף א-ב, ס"ק ז, ח, ט ו־יב, וביה"ל ד"ה טוָאן וד"ה וישראל; ביאורים ומוספים דרשו, 19]