If your child is also an EU/EEA citizen and you have right of residence in Sweden, your child also has right of residence and you do not need to contact the Swedish Migration Agency when you have a baby.
If your child is not an EU/EEA citizen and you have right of residence in Sweden, your child needs to apply for a residence card.
You want to apply – Residence card for family of EU/EEA citizens
If one of the parents is a Swedish citizen
Children born in Sweden become Swedish citizens if either of their parents is Swedish.
If you have a residence permit in Sweden
If you are an EU/EEA citizen and have a residence permit in Sweden, you must apply for a residence permit for your child after they are born. The child should apply for the same permit as you and the child’s other parent have. You must also register your child’s nationality with the Swedish Tax Agency.
You want to apply – Children born i Sweden