Answer
Under the Family Code, both parents jointly exercise parental authority over their legitimate children (Article 211) — in case of disagreement, the father's decision prevails unless there is a court order to the contrary — while the mother alone exercises parental authority over an illegitimate child (Article 176). Parental authority includes custody of the child and the rights and duties to care for, support, educate, and represent the child.
The mother's sole authority over an illegitimate child is not absolute — it yields to the child's best interest when she is shown to be unfit by clear and convincing evidence. Parental authority may also be suspended or terminated on grounds such as neglect, abandonment, immorality, drug addiction, or maltreatment of the child.