It is up to you to determine which residence permit may be relevant for you to apply for.
You must familiarise yourself with the requirements for other residence permits and determine what you wish to apply for.
See the overview of all residence permits you can apply for here.
You must meet certain requirements to be eligible to apply for permits other than protection (asylum) from Norway. The main rule is that you must be a skilled worker or have lived in Norway on a valid residence permit for the last 9 months.
There are a different set of rules for who can apply for family immigration from Norway. To find out whether you are eligible to apply from Norway, use our guide on udi.no and select the alternative that best describes your situation.
You can always apply for residence in accordance with the EU/EEA regulations from Norway.
If you apply for protection and are granted collective protection, you can still apply for other types of residence permits if you wish, after you have been granted collective protection.