I was thinking about Thalassemia, but the problem is that I need his child to get the same disease and need treatment for it. (It has to be dominant or common as a recessive gene, which Thalassemia isn't in the country the story is set in.)
The reason I need it is so that my MC can find the child of the character without knowing which hospital the child was born in. (She will have legal access to medical journals and know about the disease). If anyone have an alternative way to find a two month old orphaned baby without knowing anything but the father's name, please tell me...