I have never seen an
Arab-Byzantine imitative half-follis. Foss mentions that "Engimatic folles dated 634-36 appear to be a product of these last years of
Byzantine control and resistance." He adds, "A 20-nummi (K) piece appears to belong to the same series, though its details are obscure." [Foss,
Arab-Byzantine Coins , p 14f.] So perhaps your coin
comes from the final chaotic years of
Byzantine Syria rather than the early years of the Caliphate? But the date on your coin (if we believe it) is XUIII = 627/8 which is earlier than Foss allows and right at the end of the Persian occupation period.
Still, I don't have a better suggestion.
Bill R.