Must you sit shiva for a parent even if you have had barely any contact with them their whole life?
Hamakom yinachem eschem btoch shar aveilei tzion v’yerushalayim
This sounds like a difficult situation. The halacha though is that a child sits shiva and does all of the regular things an avel does, even if the child was given for adoption and didn’t have any contact with the parent. The reason for this is because one of the reason why a child has a longer aveilus is because now the child doesn’t have the mitzva of kibud av v’em, as the parent has departed. The reason why kibud av v’em still applies to a chiold given for adoption is because one ofthe reason for the mitzva is because the child was given the gift of life and their body from the parent, and everything that the child now has is thanks to that gift. Therefore although the parent didn’t provide the child with their needs after birth, the halacha remains the same.