Is it a condition that the sufficient portion for spending the night in Mina be from the beginning of the night or from its end?

The meaning of staying overnight in Mina is to spend most of the night there, whether from its beginning or its end. So, whoever stays in Mina for more than half the night has fulfilled the obligation. Sheikh Al-Uthaymeen mentioned that staying overnight in Mina on the nights of the eleventh and twelfth (of Dhul-Hijjah) is obligatory, and spending most of the night there suffices.