Praise be to Allah.
The Islamic ruling in this case depends on asking specialist doctors. If they say that giving butter to a newborn will cause the child to die, then this mother killed her daughter by accident. If they say that it does not lead to death, then there is no sin on the mother, because she did not cause the death of her child. If the doctors are not sure whether this was the cause of death or not, then there is no sin on the mother in this case either.
Based on this, it is essential to ask those who are expert and have knowledge of such matters.
Shaykh ‘Abd al-‘Azeez ibn Baaz (may Allaah have mercy on him) said:
If she is not sure whether the child died because of her, then there is no sin on her, because the basic principle a person is not obligated in any way unless there definite evidence. End quote. Majmoo’ Fataawa Ibn Baaz, 22/327.
If it is proven that the butter was the cause of death, this killing is to be regarded as accidental because the mother did not intend to kill her child.
Two things are required in the case of accidental killing: diyah (blood money) and kafaarah (expiation)
In the answer to question no. 52809 we have stated that the diyah in the case of accidental killing must be paid by the ‘aaqilah (male relatives on the father’s side) of the killer, not by the killer himself, and the ‘aaqilah includes the male relatives such as the father, son, brothers, paternal uncles and so on.
The expiation is required from the killer himself, and the expiation is to free a believing slave; if that is not possible then he must fast for two consecutive months.
It says in al-Mawsoo’ah al-Fiqhiyyah (16/62):
There is no difference of opinion among the fuqaha’ that accidental killing means cases where a person did not intend either to strike or to kill, such as if a person shoots at game or a target but hits a person instead, or if a sleeper rolls over on top of a person and kills him. This means that the diyah must be paid by his ‘aaqilah and the expiation is also required. End quote.
It says in Fataawa al-Lajnah al-Daa’imah (21/245, 248)
The diyah for a child who is killed accidentally after being born alive is like the diyah for a woman, which is half the diyah for a male. The diyah must be paid to the heirs. End quote.
And Allaah knows best.