Open questions
One question, and what would settle it.
Is the Ge'ez letter payt a modification of tayt?
Why it is open. Payt writes an ejective p, which has no Semitic ancestor. It is usually explained as a sign made by altering tayt, on the resemblance of the two forms and on the position of payt late in the order, but the explanation is an inference from shapes rather than a documented act, and it competes with an account deriving both Ge'ez p letters from Greek.
What would resolve it. A palaeographic sequence for both letters from dated Aksumite material, showing whether the earliest forms of payt resemble tayt more closely than the later ones do, would test the derivation directly.
Field. Ethiopian epigraphy and Semitic palaeography