The son of Draco Malfoy and Astoria Greengrass. Scorpius greatly resembles Draco (DH/e, CC).
An only child, Scorpius with his mother and father lived apart from the wizarding world, due to Astoria’s illness (CC4.4). To the disapproval of his grandparents, Lucius and Narcissa Malfoy, Astoria raised Scorpius to be tolerant and have respect for Muggles (Pm). However, due to their secluded lifestyle, the rumour arose in the Wizarding World that Scorpius was the son of Voldemort rather than of his father (CC1.3, CC1.4, CC4.4).
Although very close to his mother, Scorpius looked forward to going to Hogwarts and making friends his own age (CC2.6). Funny, and smart, he and Albus Potter became best friends with after their initial meeting on the Hogwart’s Express (CC1.3, CC2.6) and were sorted into Slytherin House (CC1.4). The loss of his mother during their third year brought Scorpius and Albus even closer together.
More to follow....
Other canon notes and references
Scorpius attracts nicknames. Some names he calls himself: "Scorpius the Dreadless" and "Malfoy the Unanxious" (CC3.14) and others are given to him: "The Scorpion King" (CC3.2, CC3.4, CC3.5, CC4.14) and "Bread Head" (CC3.14). The hurtful epithet "Son of Voldemort" is written by other students on his trunk (CC1.10).
Like all of the Black family, Scorpius is named after celestial bodies (which in turn are named after mythological figures) - Scorpio after the constellation (the scorpion that battled Orion), and Hyperion after Saturn's moon (one of the Titans).
After everything gets back to normal, Scorpius says he is thinking about trying out for the Slytherin Quidditch team (CC4.14). Is this because he knows that in one timeline he was talented enough to be their Seeker? It may also be a way to get closer to Rose Granger-Weasley.