There are several heroic qualities that are similar between the characters of Oedipus and Troy Maxson. The typical qualities of a tragic hero are strength, cunning, and pride (hubris). These qualities allow them to succeed in a variety of ways but the trend of hubris leads to their downfall.

They are both strong, physically, as Troy is a former athlete and described as a physically imposing man and Oedipus is clearly a powerful king who was able to physically overcome his father, the former king. Additionally, they both possess intelligence and cunning. Troy clearly has plans to improve his lot, wanting to become a driver and frequently asking his boss why blacks aren't allowed to drive the trucks, challenging his authority. Oedipus is also cunning, as he leads the country with intelligence, and overcomes the sphinx's riddles.

Most importantly, however, their hubris, or pride, define them as tragic heroes. Obviously, Oedipus had pride issues, killing a man over his mockery of his parentage, and eventually his pride led to his destruction when he refused to heed Tiberias's advice and sought to ensure his rule by finding the former king and ensuring his death—which revealed who he was and what he had done. Troy was a victim of hubris as well as he engaged in an ongoing affair and thought himself better than and above his family. His child out of wedlock proves his undoing as his wife denounces him even though she vows to raise the motherless child.

Oedipus and Troy Maxson of Fences both share a characteristic of tragic heroes—they falsely believe that they can defeat fate. Although Teiresias, the blind seer, tells Oedipus that he, Oedipus, killed Laius (his real father) and married his own mother, Oedipus refuses to believe the all-knowing seer. He reacts to Teiresias's revelations with anger and a lack of acceptance. Later, when Oedipus learns the truth, it is too late to save his mother. She has hanged herself, and he blinds himself in response.

Similarly, Troy believes that he can outwit death, which is his fate, by putting up a wall around his house. However, in the end, death finds him, and he can't escape fate. Like Oedipus, Troy reacts with anger to people who tell him the truth, not only about fate but also about his own family. In response, Troy, like Oedipus, is distanced from his family and dies estranged from his son and to some degree from his wife, Rose.

I would say that one of the primary heroic attributes in both protagonists is their relationship to their families.  On some level, they both support and yet fail their families.  Troy is a provider and does believe in the basic outline of financially supporting his family and acting as its head in title, but there is an emotionally supportive role that is missing. Oedipus certainly supports his family, but unknowingly betrays it in marrying his mother and killing his father.  At the same time, I would say that another similarity between both figures is the sense of unease that seems to permeate the relationship between themselves and their worlds.  It seems as if their interactions with the world and themselves are out of synchronicity and are disjointed.  For Troy, this barrier might be caused by sociological reality and his own background, while for Oedipus, this is a state of affairs as to why Thebes suffers from a plague and his role in this suffering.