What is the legitimate way to divide the blood money paid as compensation for the death of a sister during childbirth due to a doctor's error, between her infant daughter and her father, and are there any other beneficiaries entitled to this money?

The blood money (diyah) is distributed among the heirs like the rest of the inheritance. The heirs must be identified before distribution to determine each heir's share. The husband receives one-fourth due to the presence of the daughter, and the daughter receives half, based on the Almighty's saying: "And for you is half of what your wives leave if they have no child. But if they have a child, for you is one fourth of what they leave, after any bequest they [may have] made or debt." (An-Nisa/12), and the Almighty's saying: "Allah instructs you concerning your children: for the male, what is equal to the share of two females. But if there are [only] daughters, two or more, for them is two thirds of what he left. And if there is only one, for her is half." (An-Nisa/11). If the deceased has no father or mother, the remaining amount (one-fourth) goes to the 'asabah (agnate heirs) such as full brothers, with the male receiving a share equal to that of two females, then paternal half-brothers, and so on, according to the order of the 'asabat. The court undertakes the distribution of the inheritance after the death is announced and the heirs are identified.