Why is sugar important to test the relevance of sugar in fermenatation?

The way the question is worded is confusing to start. I’ll answer it based on what I think is being asked. I am assuming you are talking about yeast driven fermentation of sugar to alcohol. In order to prove that sugar is involved in fermentation you would need a solution containing sugar and one without sugar. You would then add your yeast and give them time to do their work. At the end of the alotted reaction time, check for alcohol, which is a by product of this sort of fermentation. No alcohol equals no fermentation. You will find the solution without sugar also has no alcohol (and probably dead starved yeast). The sugar is important because it is the substrate of the fermentation process.