Well, there was Alexander the Great's successor and supposed son (he was an infant in any case), Alexander IV, who was sent back to Macedonia when he died under the Regency of Perdiccias, the commander of the companion cavalry. However, Alexander's supposed last words were "ως Κρατερόι" (to Crateros – the commander of initially the largest part of Alexander’s force – the phalangites) or “ως Κρατερoι”, because the difference between “to the stronger” and “to Craterus” is only one stressed Omricon. Regardless of this, the other generals appear to have decided to hear “to the strongest” (Κρατερoι), forming the groups that would form the three Diadochi successor wars. Some believe that Alexander left specific secret instructions to Crateros as his regent, and this theory would discount the idea that his “son” Alexander IV was actually his regent, but this theory is indeed tenuous. Moreover, I do not believe that the child was Alexander’s son, as many of the major sources do not mention him, and it’s too much to Perdiccias’ favour – he used the fact that he was the regent of Alexander’s “son” to launch a pre-emptive and disastrous strike against Ptolemy Kauranos (Lightning bolt) in Egypt. I’ve not heard about this illegitimate son; the only “son” that I had heard of was Alexander IV, who was born to a concubine supposedly after Alexander the Great’s death. It would not surprising if he did have so many children – the elite of any empire almost always produce hundreds of children by the amount of women that they and their leftentants  take as concubines.