Have a look at the syntax.
You may have noticed that '*' is handled as binary operator. Thus it 
must stand between two arguments.
This is why you get the inverted question mark that shows that there 
is an error in parsing the formula text.

Two have a '*' as superscript you have to use either
  a^{{}*{}} 
(preferred since the * will still be from the StarSymbol/OpenSymbol 
font)
or you have to quote it as a string
  a^"*"
(here the '*' will be displayed with the font used for text).

TL->MRU: Please close this one.

Thanks, it worked BUT this is almost impossible for an average user to 
figure out. May I suggest a new entry in the superscripts section that  
takes a complex conjugate of something. 

I don't think, that a new entry would be a good solution.
As long as "*" is a binary operator, you have to place it in quotes
for the described use.

Closed.