The Collaborative International Dictionary
Asquint \A*squint"\, adv. [Cf. Askant, Squint.] With the eye directed to one side; not in the straight line of vision; obliquely; awry, so as to see distortedly; as, to look asquint.
Douglas Harper's Etymology Dictionary
early 13c., "obliquely, with a sidelong glance," of uncertain etymology; from a- (1) + "a word corresponding to Du. schuinte 'slope, slant' of the independent use of which no instances survive ..." [OED]. "Middle English Dictionary" compares French équinter "cut to a point;" French dialectal (e)squintar "cast a glance, look furtively."
Wiktionary
a. Looking sideways, as though warily. adv. With narrowed eyes.
WordNet
Usage examples of "asquint".
Hippolyte spoke up without rancor, even with a simple smile, his face asquint as usual.
He stood with tiller in hand, keen eyes asquint against the sky, watching the sail and calling sharp commands which the others instantly obeyed.
He now stood in the sun, his small pig eyes all asquint, trying to work out how this unexpected demand might be turned to his advantage.
Bezu walked with him part way down the street, and then, looking up at the sky, eyes asquint in the quickly fading daylight, wished him a good journey and hurried back to his hovel.
Eyes asquint against the rush of wind and her upper lip lifted, a hand held near her ear to keep her rippling silk head scarf from flying away.
There are, questionless, both in Greek, Roman, and African Churches, Solemnities and Ceremonies, whereof the wiser Zeals do make a Christian use, and stand condemned by us, not as evil in themselves, but as allurements and baits of superstition to those vulgar heads that look asquint on the face of Truth, and those unstable Judgments that cannot consist in the narrow point and centre of Virtue without a reel or stagger to the Circumference.