during the morning; in the morning
Refers to the time period of the morning; somewhat literary or old-fashioned. In modern casual speech, 朝のうち or 午前中 are more common.
あさまのうちに用事を済ませた。
I finished my errands during the morning.
Compound of 朝 (あさ, 'morning') and 間 (ま, 'interval, time'). The exact historical derivation is uncertain, but the word is now rare.