What is the ruling of Islamic law regarding the death of a child, where the cause may have been medical malpractice by a female doctor or the supervising staff or both, knowing that the doctor suspects the error originated from her?

A doctor is responsible for any mistake he makes towards a patient. Islamic law has affirmed the principle of medical responsibility. A person who is completely or partially ignorant of medicine is liable for the consequences of their actions and is sinful for their transgression. As for unintentional error, there is no sin in it, but the perpetrator is obliged to guarantee what resulted from it. If a doctor masters his work and gives the profession its due, he is not liable for any harm that occurs without his direct involvement. Based on what you mentioned regarding your doubt about transfusing blood of a different type to a child, you are liable for what happened and sinful. The expiation for this is fasting for two consecutive months, and the child's blood money is incumbent upon your 'aqilah (male relatives on your father's side). As for the supervising doctors, they are sinful for their negligence but are not liable because they did not directly commit the error. The direct perpetrator takes precedence over the cause in terms of liability.