Imam Malik (rahimahullah) was asked about bringing children to the masjid. He said: “If they do not cause a disturbance by playing around, and will stop when told to, then there is no harm. However, if they play around and disturb others, then they should not be brought to the masjid.” (al-Mudawwanah, 1/195)

Shaykh Ibn al-‘Uthaymin (rahimahullah): “Children may be brought to the masjid when they have reached the age of discernment, and children differ in reaching this age: some at the age of five; some at the age of six; and most at the age of seven. That is why the Prophet told us to command our children to pray at the age of seven. However, even if they are children older than the age of seven but they cause disturbances in the masjid, then we say to the parent: ‘Either prevent your children from coming to the masjid or control them.'” (Liqā’ al-Bāb al-Maftūh, no. 13)

Shaykh al-Albānī (rahimahullah): “If older children play and run around in the masjid, then it is upon the fathers and guardians to discipline them and command them to stop. Otherwise, those in charge of the masjid should remove them from the masjid and this is what ‘Umar [ibn al-Khattab] used to do, as mentioned by Hafidh Ibn Kathīr. (al-Thamr al-Mustaṭāb, pg. 761)