\documentclass{article}
\begin{document}
A$^c$

A$_d$

A$^c_d$

A$_d^c$


$^aA$

$_bA$

$^a_bA$

$_b^aA$

$_b^aA^c_d$

$_{x<3,>0}$

$^{\prime\prime\prime}$

% Advanced 
% chemistry use for ion
$\mathrm{Na}^+$ 

% second derivative
$\psi^{\prime\prime}$

% mathord in prescript
$ _{\mathord{x}}\mathord{G} $

% anyop expression example:
$ a^{= x}$

% fenced scripts
$ a ^{(1)} $
$ a _{(g)} $
$ a ^{(\neq 0)} $
$ a _{(>0)} $

% scripts with trailing puncts
$ a_{n.n.n.} $
$ b^{n.n.n.} $
$ a_{i,j,} $
$ b^{-,} $
$ a_{k,} $

\end{document}
