Ah, the emphasis becomes a bit clearer with the full quote.
I knew nothing except what I gathered from Time magazine and reading everything I could lay my hands on at home, but as I inched sluggishly along the treadmill of the Maycomb County school system, I could not help receiving the impression that I was being cheated out of something. Out of what I knew not, yet I did not believe that twelve years of unrelieved boredom was exactly what the state had in mind for me.
Reading the sentence before, and if you imagine a comma after the "what", then it becomes clear that Scout is commenting that she is being cheated out of something. She doesn't know what it is, but she knows she's being cheated, and that she does not believe that the point of twelve years of schooling is just to bore people, so there is something that she's missing.
Just to be clear, I don't think she's necessarily saying that someone is intentionally cheating her out of actually learning something in school, but rather that she just doesn't understand it. It could be personal limitations or an epiphany she has not yet reached (sometimes, things just "click" later in schooling), or she could be seeing the effects of society at the time where women often didn't receive the time and attention in education that men did since it was assumed that women would marry and become mothers, and therefore it wasn't necessary to educate them as well.