Vanilla sugar is best made using whole vanilla beans.
Vanilla paste has a much more intense flavor than vanilla extract. It can be used to make vanilla ice cream or vanilla butter cream frosting. It would also be great for producing sauces like creme anglaise or sabayon.
The paste will be speckled with the black specks of vanilla, giving your product visual appeal as well as flavor.
You're right you can't make it with vanilla extract, but I thought you said you had vanilla paste. I've never worked with it but I assume that you can mix it in with the sugar, probably in a food processor and it will keep well.
"You are what you eat, so don't be fast, cheap, easy, or fake."
You make vanilla sugar by putting bean pods in the sugar and letting the aroma molecules (volatile oils) permeate the sugar -- takes a few weeks at least before the sugar gets up to speed. Anyway, it's dry into dry.
Vanilla paste is like tar. Mixing it with sugar would just make a big mess.