Imam al-Shafi'i (may Allah have mercy on him) said: "The saying of Allah, the Mighty and Majestic, 'from among your men' [Surah al-Baqarah: 282] indicates, and Allah knows best, that the testimony of children is not permissible in any matter; also because only adults, not those who have not reached puberty, are addressed with the obligations; and also because they are not among the witnesses who are approved of, and Allah Almighty has commanded us to accept the testimony only of those whom we approve of."
The Shaykh (Imam al-Bayhaqi) (may Allah have mercy on him) said: "And it has been narrated to us from the Prophet (peace and blessings be upon him) that: The pen has been lifted from three: from the child until he reaches puberty, from the insane until he recovers, and from the sleeper until he wakes up."
Imam al-Shafi'i (may Allah have mercy on him) said: "Then if someone says that Sayyiduna Ibn al-Zubayr (may Allah be pleased with him) declared it (the testimony of children) permissible, then (the reply is that) Sayyiduna Ibn Abbas (may Allah be pleased with them both) rejected it."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الشهادات / Q20609
Amr bin Dinar narrates from Ibn Abi Mulaykah (may Allah have mercy on him) that he wrote to Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) asking about the testimony of children. He wrote in reply that Allah Almighty says: 'from among those whom you approve of as witnesses' [Surah al-Baqarah: 282]. "These are not approved witnesses, so their testimony is not valid."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الشهادات / 20610
Ibn Jurayj narrates from Abdullah bin Abi Mulaykah that he said: I sent a message to Sayyiduna Ibn Abbas (may Allah be pleased with them both) to ask about the testimony of children. He replied that Allah Almighty says: 'from among those whom you approve of as witnesses' [Surah al-Baqarah: 282]. These are not among those whom we approve of.
I sent a message to Sayyiduna Ibn al-Zubayr (may Allah be pleased with him) and asked him the same question. He said: "It is likely that if they are asked, they will tell the truth." He said: I have not seen judgment given except according to what Sayyiduna Ibn al-Zubayr (may Allah be pleased with him) said.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الشهادات / 20611
Hisham bin Urwah (may Allah have mercy on him) says that Sayyiduna Abdullah bin al-Zubayr (may Allah be pleased with him) used to give judgment concerning injuries on the basis of the testimony of children.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الشهادات / 20612