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, though you could omit the hyphen before “AD” (see CMOS 7.96, sec. 1, “number + abbreviation”). And in contexts that exclude mention of BC centuries, the “AD” could be taken for granted and omitted. See also CMOS 7.94, which gives you permission to omit the hyphen between “early” and “fourth.”