You might be elligible for a residence permit on the basis of being a parent of a child under the age of 18, if your residence in Iceland is necessary for the child to continue living in Iceland. You must be the biological or adoptive parent and have custody of the child (either full or shared custody) and intend to live with your child in one home.

You might also be elligible for a residence permit to maintain contact with your child despite not intending to live with your child. In this case you must have had a previous residence permit on a different basis that cannot be renewed due to changes in circumstances. Furthermore, you will be asked to prove that you have regular access to your child, for example by submitting an agreement of a child's access.

Keep in mind that there are other requirements that must also be met.