The Arabic root cited for taʿmiyya’s taste-and-food meaning is Ṭ-ʿ-M.
In Arabic script, the root is ط-ع-م. It is associated with ideas of taste, food, and eating, and appears in related words such as ṭaʿām, meaning “food,” and ṭaʿm, meaning “taste” or “flavor.” The Egyptian name taʿmiyya is explained as a diminutive or singulative form connected with this root.
That linguistic background helps explain why taʿmiyya can be understood roughly as a small piece of food or a small tasty morsel. In Egypt and Sudan, the term commonly refers to the local form of falafel, usually made from ground fava beans rather than the chickpeas more typical of Levantine versions.
This root should not be confused with the etymology of falāfil itself, whose origin is disputed and has been linked to words for pepper or small round objects. The question concerns taʿmiyya specifically, so Ṭ-ʿ-M is the single relevant answer.