How to change the position of a single letter/symbol (*) – gender specific typography

Raise the asterisk by 1ex minus the height.

\documentclass{article}
\usepackage{fontspec}

\setmainfont{Alegreya}

\newcommand{\gs}{\raisebox{\dimexpr1ex-\height}{*}}

\begin{document}

\makebox[0pt][l]{\vrule height\dimexpr1ex+0.05pt depth -\dimexpr1ex-0.05pt width 3cm}%
\makebox[0pt][l]{\vrule height 0.05pt depth 0.05pt width 3cm}%
x Autor\gs in

\end{document}

You may want to \renewcommand{\*}{...} instead of \newcommand{\gs}{...}, but this might break other (rare) uses of \*.

I believe you're looking for the \textasteriskcentered macro. Depending on the text font you employ, you may need to combine it with a suitable \raisebox "wrapper" instruction -- you're obviously free to choose a snappier name than \genderstar -- in order to get the desired vertical placement.

%% compile with either XeLaTeX or LuaLaTeX
\documentclass{scrartcl}
\usepackage{fontspec}
\setmainfont{Adobe Jenson Pro} % optional
\newcommand\genderstar{\raisebox{-0.2ex}{\textasteriskcentered}}

\begin{document}
x Autor*in 

x Autor\textasteriskcentered in 

x Autor\genderstar in
\end{document}