Works in all math styles...can easily choose scale by changing Vert/Horz. stretch parameters shown as .6 and .5. Line thicknesses will always be good, since this is composed from an overlay of - and \vert in the appropriate math style.
\documentclass{article}
\usepackage{stackengine,scalerel}
\newcommand\newperp{\mathbin{\ThisStyle{\setbox0=\hbox{%
\abovebaseline[-\dimexpr.5\LMex+.2ex]{%
\ensurestackMath{\stackengine{-\dimexpr.6\LMex+.2ex}%
{\SavedStyle\hstretch{.6}{-}}% ADJUSTABLE V SCALE
{\SavedStyle\vstretch{.5}{\vert}}% ADJUSTABLE H SCALE
{O}{c}{F}{F}{S}}}}\dp0=0pt\box0}}}
\begin{document}
$A\newperp B$
$\scriptstyle A\newperp B$
$\scriptscriptstyle A\newperp B$
$A^{\newperp}_n$
\end{document}

Changing stretches to .7/.6 changes result to
