Domain transfer

By transfer your domain extension, do you mean transferring the registration of your domain to AWS? You can learn more about doing so here: https://docs.aws.amazon.com/Route53/latest/DeveloperGuide/domain-transfer-to-route-53.html

Thanks for the info. Yes I want to transfer my domain to AWS but I can't locate and verify my domain in the list.

If your top-level domain (TLD) is not in the list of domains that the Amazon Route 53 Registration service supports, you cannot use this functionality with that particular TLD.

You can still configure Route 53 as the zone provider for your zone, while maintaining the domain registration somewhere else.