It's impossible to give any answer to this question without distorting the historical record. The concept of "nationality" did not exist in Alexander's day; there are a range of people in his immediate ancestry about whom very little is known; his own family worked hard to enforce claims to a particular ancestry that were only rarely recognised by others. It is impossible to say to what people or culture Alexander "belonged" even in his own time, because of the political interests at stake. Layer on top of this the creation of entirely new, artificial nation-states in the 19th and 20th century that each had an interest in laying claim to historical figures to boost their national identity and collective narrative, and you have yourself a spectacular cocktail of belligerent anachronisms.