Is a person sinful if he leaves his infant child crying during prayer or recitation of the Qur'an, or at night due to exhaustion and fatigue?

If the child's crying is not due to hunger or illness and does not result in harm, there is no sin upon the mother for letting him cry, and she is not obliged to silence him. It is permissible to carry a child during prayer and recitation, following the example of the Prophet (peace be upon him) who prayed while carrying Umamah bint Zaynab. It is also legislated to shorten the prayer if the crying of a child is heard, out of compassion for him and his mother, as the Prophet (peace be upon him) did.