If you're trying to add your YouTube Channel on your profile but for some reason you're not getting any results this is due to a few reasons.
New Channel/Username Change
If you just created your channel or made a name/username change it could take a few days for the channel to show up in the dropdown. You can read more about this here.
Privacy Visibility
Another reason your channel may not be showing up is that you have your channel/content hidden. You can change these settings in your Google Account. You can read more about this here.