Here's a pic of a Ptolemaic late bronze coin (Svoronos 1696, ca 30mm, ca 15gm) which was described by Svoronos as depicting a 'petasos' in the left field next to the eagles. Not perfect but this is a decent specimen for the type. Later period Ptolemaic bronzes declined in their manufactured quality.
Based on this discussion and some other comments it seems it may well be instead a kausia. There are smaller relatives of this coin type (not catalogued in Svoronos) with the same little 'figure' that seems to be the kausia. Cox 119 has one eagle (24mm, 8gm) and there's a small 2-3 gram variety as well. The 'hat' looks the same on all three sizes.
One thought was that the kausia was a symbol of the Ptolemies' Macedonian heritage but there are some other coins that clearly depict a Corinthian helmet so other ideas for this 'hat' can't be excluded so...
With such a small
engraved image there must be considerable uncertainty attached to the specific form of headdress (if it is a hat at all). However, I am in the same camp as
Svoronos and would describe it as a probable
petasos, rather than a
kausia.
The key aspects in this determination are the apparent dimple on the top of the hat characteristic of many depictions of the
petasos, but not the
kausia, plus the presence of narrow protuberances beneath the base of the hat which appear to be an attempt to depict the fastenings or ties for the
petasos.
As for the
kausia being a symbol of Macedonian heritage, I think that for the reasons outlined by Kingsley this is one of the great myths of numismatic interpretation. The written record states clearly that only the Athenians, for a very narrow period of time, regarded the
kausia as indicative of Macedonian origin, only by virtue of the fact that this
type of hat was worn by Macedonian veterans garrisoning the city at times during the wars of
Diodochi in the thirty years following the death of
Alexander the Great.
These Macedonian veterans of course returned from the anabasis wearing the kausia as a unique badge of identity associated with their campaign in Bactria and the Indus Valley. Within a generation the characterisation and for the most
part the hat itself disappeared from the Greek historical record.
In the case of the coin of Antimachos I bearing the
kausia the same erroneous argument is often run that this signifies
his Macedonian heritage. However, consider the fact that until the time of Eukratides I (contemporaneous with Antimachos I) all
Baktrian kings,
bar one, were portrayed on coinage without headdress, but for the royal diadem. The exception was of course Demetrios I, who is portrayed wearing the
elephant skin headdress signifying
his conquest of the regions south of the Hindu Kush (
India as it was then called). With the early
success of Eukratides I, he moved from the conventional portrayal (sans hat or helmet) to one bearing the adorned Boeotian helmet of the cavalry commander, symbolic of
military success. At this stage Antimachos appears on the scene, the last of the Euthydemid line
confronting Eukratides in the domain of Arachosia and the Paropamisadai, south of the Hindu Kush. It is in the region that the chitrali was inferred to have originated, derived from an ancient headdress. Any wonder that in opposing Eukratides I, Antimachos sought to align himself with the local populace rather than the Macedonian conquerer wearing the headers of
military command and conquest?
Identification with the conquering and warring Macedonians is the last thing a local ruler would want under the circumstances that prevailed at the time.
Therefore I posit, contrary to popular numismatic myth, that
the kausia worn by Antimachos is most likely an attempt to emphasise his local affiliations and sympathies, as a ruler of parts of Arachosia and the Paropamisadai, in contrast to that of the usurper Eukratides who is portrayed on
his later coinage wearing the Boeotian cavalry helmet, typical of the Macedonian conquerers of
Baktria. A sign of Macedonian heritage the
kausia most certainly is not!