Is it from the Sunnah of the Prophet (peace be upon him) to allow children to cling to him during prayer, and what is the evidence for that?

The Prophet, peace and blessings be upon him, used to pray while carrying Umamah bint Zaynab. When he prostrated, he would put her down, and when he stood up, he would pick her up. Abdullah ibn Shaddad narrated from his father that the Prophet, peace and blessings be upon him, came out to them carrying either Al-Hasan or Al-Husayn. He put him down, then said the takbir for prayer, and prolonged one of his prostrations. When the Companions asked him about it, he replied that his son had mounted him, and he disliked to rush him until he had fulfilled his desire.