If I was to mix barium sulphide (BaS) and barium carbonate in equal amounts with some water to make a paste and applied to the skin will it burn ? If not will it burn the skin if left on it for 20 minutes?
Would this mixture give a chemical burn ? Or any other effects ?

Yes, it is commonly used as a depilatory but can be poisonous if ingested. What are you trying to do?

In some combinations I saw where it is used in permanent hair removal, so combinations and percentages may have some bearing.

Most warnings were about breathing and digestion of the chemical.

As with any chemical, it was not made to be put on the skin and should not be.