Why does this throw an error for double subscripting?

I'm listing two possible solutions. In the first solution, I employ round parentheses to provide some visual clues for readers.

\documentclass{article}
\usepackage{amsmath}  % for \text directive
\usepackage{bm}       % for \bm directive (\bm more robust than \boldsymbol)

\begin{document}
$(\widehat{\bm{\Sigma}}_{\hom})_{jj}^{1/2}$
\quad\text{or}\quad
$\widehat{\bm{\Sigma}}_{\hom}{}_{jj}^{1/2}$
\end{document}

Don't use \mathbf for Greek letters, hope the below code may meet your expectation:

\documentclass{book}
\usepackage{mathtools}
\begin{document}

$\boldsymbol{\hat{\Sigma}}_{{\mathrm{hom}}_{jj}^{1/2}}$

\end{document}