The correct answer is of.
The preposition of is used to indicate possession, origin, or a part of something. In this case, the mother is aware of her children, meaning that she knows about them and is familiar with them.
The preposition at is used to indicate a location or a point in time. In this case, it would not make sense to say that the mother was aware at her children.
The preposition over is used to indicate control or dominance. In this case, it would not make sense to say that the mother was aware over her children.
The preposition on is used to indicate a surface or a location. In this case, it would not make sense to say that the mother was aware on her children.