out (of) the corner of (one's) eye
Of something seen, in one's periphery; partially and/or fleetingly, as opposed to fully and for an extended amount of time. Out the corner of my eye, I saw something moving in the bushes, and it turned out to be a stray cat. Sarah caught Tommy kissing Jessica out of the corner of her eye.
out of the corner of one's eye
Glancing casually or surreptitiously, as in Out of the corner of my eye I saw Justin walking out the door. This expression refers to looking sideways at something rather than directly.