Modernism is a broad label applied to a literary and artistic movement that began around the early 1900s. Modernist stories often feature non-linear narratives, fragmentation, and internal monologues (like when we read Sarty's thoughts). In terms of the time frame of the story, "Barn Burning" is linear chronologically. It seems to move from day one to day seven in a straight line through space-time. But this is not quite true. The narrator also inserts pieces or fragments of Sarty's future life, and of Abner's past into the mix, resulting in what is considered a healthy confusion on the part of the reader.
This is also a coming-of-age story because Sarty has to choose between being his father's son and leaving home at the age of ten to make it on his own. Sarty doesn't come-of-age in the legal sense – he doesn't turn eighteen. He does, however, take on a variety of adult roles, and considers himself obliged to act by a specific code of morality. For Sarty, this movement from child to adult is at a dramatic peak that occurs during the week in which the story is set, culminating in his leaving home.
All this is intensely psychological. Sarty and his father are locked in a struggle of differing values and ideals. Each of them waits to see what the other will do next. Sarty's age makes this particularly compelling. He might act like an adult, but he's just a kid. We can't forget that. This creates suspense in "Barn Burning" in part because both the reader and the narrator know things Sarty doesn't. This technique is called dramatic irony. It's often used to build suspense.
Take horror movies for example. The person watching the movie knows there's a monster behind the door, but the character doesn't. The person watching gets tense waiting to see if the character will open the door. In "Barn Burning" the dramatic irony is subtler. For example, we guess that Abner will burn the de Spain barn down far before Sarty realizes this. Overall, the situation in "Barn Burning" is so tricky, we don't quite know what we want Sarty to do. We might not even be sure how we feel about Abner's barn burning.