I am trying to scale up the radius of skin modifier, but when I am hitting CTRL+A I unselect the vertex. How can I scale it up without this key shortcut?
If you changed the default CTRL + A key shortcut to something else, I don't think you'll be able to scale the radius of a skin modifier mesh. Another reason why I force myself to adhere to default key shortcuts.
I recommend reverting your shortcut keys to default to get back that functionality with the skin modifier.
It was an issue with Interaction preset, you can choose it when you launch the blender. I choose Maya, because I work in it at work, but it was mistake, it does not work correctly.