The following code results in the 'j' being too far away from the parenthesis:
\documentclass[a4paper, 12pt]{article}
\usepackage[english]{babel}
\usepackage{amsmath}
\usepackage{fontspec}
\setmainfont{STIX Two Text}
\let\arrowvert\undefined
\RequirePackage[stix2]{newtxmath}
\let\openbox\undefined
\DeclareSymbolFont{operators}{OT1}{stix2}{m}{n}
\SetSymbolFont{operators}{bold}{OT1}{stix2}{b}{n}
\newcommand{\p}[1]{\left({{}{#1}}_{{}}\,\negthickspace\right)}
\title{Untitled}
\date{Typeset on \today}
\begin{document}
\maketitle
$$ D_{v_p} = \p{ {\widehat e}_i }_{j} $$
\end{document}
Upon commenting the STIX-related code, the problem seems to disappear. Replacing it with \usepackage{unicode-math} produces the same artifact.
What is wrong?
\left(and\right)? to encase\hat{e}_i(or\widehat{e}_i)? Put differently, why not write(\widehat{e}_i)_jor, if you prefer,{(\widehat{e}_i)}_j-- and obtain nicely spaced subscripts?unicode-math. So it's impossible to say why your attempt with unicode-math didn't work without seeing the code. Currently theunicode-mathtag and title are a bit misleading since the question is mostly about what happens with legacy math.