[1] Of Barsine, Mary Renault states that: No record at all exists of such a woman accompanying his march; nor of any claim by her, or her powerful kin, that she had borne him offspring.
That he actually did marry another Barsine [Stateira, often referred to in Greek sources as Barsine] must have helped both launch and preserve the story; but no source reports any notice whatever taken by him [Alexander] of a child who, Roxane's being posthumous, would have been during his lifetime his only son, by a near-royal mother.
Renault concludes that the romance with Barsine was invented retrospectively to validate Heracles' parentage.
[3] On Alexander's death Nearchus, who was then son-in-law of Barsine, advocated for Heracles' inheritance, but was unsuccessful.
At that point Polyperchon, a regent of Macedon who had been replaced by Cassander and had all but disappeared for the previous six years, began championing Heracles as Alexander's true heir, and Polyperchon began forming an army.