\documentclass{article}
\begin{document}
$$ f_a,  f^a, f_a^a, f^a_a $$

$ {}_a$,  ${}^a $

\[ \mathop{A}\limits_B\limits^C \qquad
   \mathop{A}\limits^C \limits_B \qquad
   \mathop{A}\nolimits_B\limits^C \qquad
   \mathop{A}\nolimits^C \limits_B
\]
\[ \mathop{A}\limits_B\nolimits^C \qquad
   \mathop{A}\limits^C \nolimits_B \qquad
   \mathop{A}\nolimits_B\nolimits^C\qquad
   \mathop{A}\nolimits^C\nolimits_B
\]

\[ \mathop{\mathop{A}\limits_B}\limits^C \qquad
   \mathop{\mathop{A}\nolimits_B}\limits^C \qquad
   \mathop{\mathop{A}\limits_B}\nolimits^C \qquad
   \mathop{\mathop{A}\nolimits_B}\nolimits^C
 \]
\[
  \stackrel{C}{{\stackrel{B}{A}}}
\]

\end{document}
