This term is frequently found in early English and colonial New England (and perhaps other) last will and testaments when referring to bequests to or care of surviving children -- that is, those not having reached their majority. For example, "Allyn Reade and Jacob Willett to be overseers and guardians to my children during their nonage."

As a confusing factor, the same word, Nonage, was sometimes used as a shortened version of Nonagium (Latin), which in traditional English law refers to a "ninth part of of movables" paid on death to the clergy of the local parish on the pretense of being distributed to pious uses. However this usage in English documents is believed to both rare and not easily confused with the above usage.

Source:Black's Law Dictionary, 4th Edition