The circumstances of Hassan's birth, antecedent action in the novel, directly or indirectly drives the events of the narrative. His guilt over fathering Hassan but not claiming him determines Baba's relationship with Hassan and also with Amir, the son he does acknowledge. Baba is especially kind and gentle with Hassan, a mere servant, for reasons that Amir cannot understand; in contrast, Baba is demanding and distant with Amir. Baba's treatment of his two sons creates in Amir a deep insecurity and jealousy that leads to his two betrayals of Hassan, his friend. The subsequent shame and self-hatred almost destroy Amir.
The relationship between Baba and Amir changes, however, and the change directs events once they immigrate to California and make a new life. Baba does love Amir, which Amir comes to realize, first during their dangerous escape from Afghanistan and later when he watches his father struggle to support them. Living in poverty brings them together as they work side-by-side to eke out a living. Baba's love for Amir is further demonstrated when he acts to help Amir realize his marriage to Soraya. Because the relationship between Baba and Amir has changed so profoundly, Amir and Soraya make a home for Baba and care for him with great tenderness while he is dying.
well, the father son relationship has an important influence on the characters that eventually effects the events of the novel as well. Amir's obsession and his attempts to gain his father's love was the main reason for his jealousy due to the fact that Hassan was always better than him in doing that. As a result, Amir betrays Hassan by framing him that he stole his watch.
Another important example is Baba's relationship with both Amir and Hassan. Due to the fact that they are both their sons he treats each one differently because of societal influences. This eventually effects Baba's character and causes him into being a hypocrite. It affects Amir, as well because he realizes that his life was based on lies nothing else making it even harder to forgive his father although he had done a huge mistake as well when he was a child that had ruined his life as well as his father's.