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Certainly NOT "son of".
The word Ayt, most of the time spelled ait following French transcription, simply means "those of" i.e. The pople of... It designates a group in varying order of importance and number, from just a family name to the equivalent of a clan, to a territorial confederation of local governments (which in old fashioned sociological descriptions is sometimes referred to as "tribe" which means nothing in anthropological terms).
Perhaps the closest term to ait (or ayt) would be the Scottish "Mac", dor "Mc".
In some cases it could also be compared to the "de" of French and Spanish, "da" of Portuguese and Italian (with di), von and van of German and Dutch, but it would refer to a territorial origin (though not the medieval reference to a place of birth such as "John of Salisbury", "Thomas of Canterbury" etc)not a lineage.
However, the term ait is plural and designates a group, not a person. The equivalent singular designation is, dependending on the region, "win" (feminine "tin"). In Tamajeq/Tamasheq (Tuareg) the masculine in is found also in toponyms, example "In Amenas" in southern Algeria, which is often confused with the Arabic ain for fountain or spring. In Amenas means "The One from Amenas" not The Fountain/Spring of Amenas from the Arabic ain. The most wellknown female example is Tin Hinan athe legendary 4th century queen and mythical ancestress of the Tuareg.
The confusion with "son of" comes from the fact that the Arabs and Arabic (administrative)practice (also adopted by the French colonial administration, tended to systematically replace ait by the Arabic "banu", "bani", "ben" for son of or sons/children of, which is central to Arabic naming convention.