Sorry I'm late replying; I needed enough spare time to search the indexes properly.
The Sear catalogue lists a dozen or so varieties of Alexander III tetradrachms with the comment that this "represents only a tiny portion" of all the known types. Not entirely helpful.

But don't give up hope yet, for your coin has one very unusual feature: the word "BASILEWS" (king) is not often found on coins of Alexander the Great - it's far more common on coins of subsequent kings also named "Alexander". And the word "BASILEWS" is also not often found
above the image of Zeus - when it's present, it's almost always either to the left, or beneath, Zeus.
In fact, searching
Wildwinds and
CoinArchives, I only found one matching type with a similar design. Both are examples of much the same coin type: from the mint of Tarsus (now in Turkey), issued during the reign of Alexander's successor, Philip III.
Yours isn't the exact type as either of these coins (the monogram beneath the throne is different, and the object to the left of the throne look different, too), but I'm fairly sure this is the correct mint city, and reasonably sure it's not a lifetime issue. Others are better equipped than I am at confirming or denying this, and at pinning down an exact attribution (catalogue number etc).
Finally, the usual caveat: being from what might be considered a "famous Biblical city" (The Apostle Paul was born in Tarsus), it's probably been reproduced more than other types. On the upside, if it's genuine, it's probably worth a bit more than your "typical" Alex III tet.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis