The affrication mark is a small stroke written beneath a Mandaic letter, and it is the mechanism by which a twenty-two letter inherited alphabet went on serving a language that acquired sounds it had no letters for. Marked ag is a voiced velar fricative, marked ad a voiced dental fricative, marked ah a pharyngeal, marked ak a voiceless velar fricative, marked ap an f, marked ash the affricates written ch and j in English spelling. The alphabet did not grow; the letters were annotated.
That is the same solution Syriac reached for with Garshuni and the same one Turoyo uses with three dots, and it is worth noticing how consistently the scripts of this family chose it. Adding letters would have unsettled the order, the count and, in Syriac and Hebrew, the numeral values that hang on the order. Adding marks costs nothing.
The reason Mandaic needed the marks is a history of contact. Iranian vocabulary entered Mandaic early and in quantity, and Arabic and Persian have shaped the modern spoken language heavily. A small community speaking a minority language inside larger ones borrows constantly, and its script has to keep up.
The marks are also optional. Ordinary writing leaves them off and expects the reader to know the word, in the same way Syriac leaves off its points. A page of Mandaic therefore records less than it could, and the reader supplies the rest.