If you want to extend your residence permit to continue living with your child in Sweden, and they have a residence permit on the basis of their need for protection, you must apply for an extended residence permit together.
If you want to remain in Sweden because you have a new family relationship, you can also apply for an extended residence permit.
If you want to remain in Sweden because you need protection, you can apply for a residence permit on the basis of your need for asylum.
You can find information and the application you need to fill in on the page You want to extend – Asylum.