All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon Prophet Mohammad and upon all his family and companions.
It is permissible to bring discerning children to the Masjid to teach them the etiquette of congregational prayer and the manners at the Masjid. Here, the father/guardian should keep the child next to him for better direction and guidance and not let him/her mess with the property of the Masjid, annoy the praying people, and consequently miss the educational purpose for which he/she was brought to the Masjid in the first place.
As for the non-discerning children, the general rule is that they shouldn`t be brought to the Masjid because they don`t know how to pray, they are hard to control, they usually disturb the praying people, they may contaminate the masjid or play with the copies of the Quran and Majid property. All these evils usually happen and the Sharia rule, in this regard, states "Warding off evil takes precedence over bringing benefits." However, if a person had no choice but to bring their child to the Majid, then he shouldn`t leave him/her alone, he should keep him/her next to him and he shouldn`t pray in the first rows. And Allah the Almighty knows best.