What is excessive constriction of the pupil called?

Miosis or myosis is excessive constriction of the pupil. The term is from Ancient Greek μύειν, mūein, "to close the eyes".

The opposite condition, mydriasis, is the dilation of the pupil. Anisocoria is the condition of one pupil being more dilated than the other.

Light entering the eye strikes three different photoreceptors in the retina: the familiar rods and cones used in image forming and the more newly discovered photosensitive ganglion cells. The ganglion cells give information about ambient light levels, and react sluggishly compared to the rods and cones. Signals from photosensitive ganglion cells have multiple functions including acute suppression of the hormone melatonin, entrainment of the body's circadian rhythms and regulation of the size of the pupil.