A fetus has a special type of hemoglobin. What is this called?

Fetal hemoglobin (Also known as Homoglobin F/HbF)

Which is the main oxygen transport protein in the human fetus during the last seven months of development in the uterus and persists in the newborn until they are roughly 6 months old. It differs most from adult hemoglobin in that it is able to bind oxygen with a greater affinity than the adult form, which gives the developing fetus better access to the oxygen from the mother's bloodstream.

It's nearly completely replaced by adult hemoglobin roughly 6 months postnatally, except in rare thalassemia cases in which there can be a delay in cessation of Hemoglobin F production until 3-5 years of age.