documentclass[12pt]{amsart}
usepackage{amsmath}

begin{document}

[
underset{circ}{(alpha_i)}^{sigma}_n
]

[
underset{circ}{(alpha_i)^{sigma}_n}
]

end{document}

documentclass[12pt]{amsart}
usepackage{amsmath,accents}

begin{document}

[
underaccent{circ}{(alpha_i)}^{sigma}_n
]

end{document}