She did not have any milk in her breasts so she fed her baby girl butter and she died
Question

                A woman gave birth to a daughter more than fifty years ago, but there was no milk in this woman’s breast, so she gave the girl butter, and after approximately six days the child died. 

Is there any sin on the mother for that? 

She is afraid that she is the one who caused her death, i.e., that the child died because of the butter. 

The mother did not know that butter would cause the child to die; if she had known that butter would cause her to die, she would not have given it to her daughter.
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.