What is the simple sudject of the following sentence? during the night, the frigteneded child call for his mother and father.

I think it's  "child" or "frightened child" , because a simple subject is the main word or word group that tells whom or what the sentence is about.

A simple subject is the basic of the sentence, it is who the sentence is about. So the answer to your questions is Child because he or she is frightened 

Already answered but thanks