Where does this star came from? [EDIT - Detailed Question]
This seems as a starred transformation. It is a discrete version of the Laplace transformation. Laplace transformation is continuous by nature. Starred transformation is discrete, and the star denotes difference between continuous and analog domain. 

This is commonly used when teaching about the Z transform. It tends to be confusing, so the teachers typically just skim over it.

Here are some explanation about it:  https://en.wikipedia.org/wiki/Starred_transform

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