vec{o}^t

vec{o}^{,t}

documentclass{article}
usepackage{esvect}
begin{document}
$vv{o}^t  vv{o^t}$
$vec{o}^{,t}$
end{document}

documentclass{article}

makeatletter
newcommand{vo}{vec{o}@ifnextchar{^}{,}{}}
makeatother

begin{document}

$vec{o}^t o$ $vo^t o$

$vec{o} o$ $vo o$

$vec{o}^t_t o$ $vo^t_t o$

end{document}

$overrightarrow{A}$  this one for simple vector
$overrightarrow{A}^{value}$  This one for superscript
$overrightarrow{A}_{value}$  This one for subscript.