Asteure in Québecois Jargon means "Lately." It's derived from "à cette heure." (which is 'at this hour')

For example:

"Qu'est-ce tu fais asteure?" (spoken) -> "Qu'est-ce que tu fais à cette heure." (written)
which translates to:
"What've you been doing lately?" or "What are you doing now" (which is more accurate seeing as it is in present tense)

Although this is Jargon, at school, I was taught this, because it is sometimes encountered in poems.