I'm not sure you do really understand what a "pseudo EOF" is all about.
First, as per the comments, there is no ASCII char greater than 256. Nor is one needed.
What you are being asked to do is to simulate this in code. Say you have a function that reads a character:
int getchar(fhandle);
This function will return values from 0 to 255 to represent ASCII characters. It can also return a special value such as -1 to indicate end of file. This special value is the "pseudo EOF".
This character is not in the file. It is returned by the function when there are no more characters in the file.