Q. Is it: early-fourth-century-AD amphora? What is proper way to handle early fourth century AD amphora?
A. V-e-r-y carefully. (You were setting me up, right?) The way you’ve styled it is fine. In contexts that exclude mention of BC centuries, however, the “AD” could be taken for granted and omitted, and CMOS 7.87 permits the omission of the first hyphen.