John Allan was not Poe's father. Even calling him "foster-father" is a bit generous. It seems like the more common term these days is "guardian." Sure, Allan helped raise Edgar Poe but, more than anything else, young Poe often felt more like a guest in the Allan household rather than a son.
So, in one sense, it makes sense that Allan would never fulfill the fatherly duty of providing support for his son after his death. On the other hand, Poe called Allan "Pa" for parts of 15 years. And, remember, Allan is an incredibly wealthy man — one of the richest in Richmond. Either way, when John Allan sat down on April 17, 1832 to write a draft (one of many) of his last will and testament, Edgar Poe was purposely excluded.
After Frances Allan's death, John Allan married Louisa Patterson on October 5, 1830. Patterson, now the second Mrs. Allan, was listed as "executrix" of the Allan estate in the 1832 will. In 1831, the couple's first son (of three) was born, who they named John Allan, Jr. Now with a legitimate biological heir, Allan Sr. had no reason to provide for Edgar Poe in his will.
Allan did, however, give money to the family of his first wife, specifically to Ann Moore Valentine — amounting to "three hundred dollars annually" throughout "her natural life." Though he ignored his "foster son" Edgar Poe, Allan did provide for his illegitimate children. Allan had fathered twins to a married woman named Elizabeth Wills in 1830 — he called it his "fault." He had struggled for some time with balancing his responsibility to them and concern for his social standing. In the end, he made the decision to do the right thing, and offered them one-fifth of his estate or $4000 each when they reached 21 years old — a social suicide which would be exposed after John Allan's death.
John Allan died on March 27, 1834. His widow was not too happy when she heard what was in her dead husband's will... More on that another time.