One thing that is the closest to certainty is that the Tetradrachms of
Lysimachos show the
portrait of Alexander, influenced by the skill and execution of the artist at the various mints which produced them. Arguments will endure about whether any of the Alexander coins show
his portrait or not, or whether a small sub-set do and others certainly do not. Debate continues. There are other threads within this
forum (a quick
search should lead you to these) as well as numerous articles and books about this subject both online and off.
Martin Price's Alexander corpus is a great place to start, if you can access a copy from somewhere. I am sure this subject will attract a LOT of responses, perhaps even arguments.
Good luck in your
search.
Walter
Holt