Changing the height of a symbol

Question

I would like to make a shorter version of $\sqcup$ to use as a symbol for a Turing machine if possible. The first picture is the height I would like it to be and the second is the default height.

Answer 1

One option, scaling down vertically the symbol:

\documentclass{article}
\usepackage{graphicx}

\newcommand\ssqcup{\scalebox{1}[.75]{$\sqcup$}}

\begin{document}

$\sqcup q_{2}\quad \ssqcup q_{2}$

\end{document}

Answer 2

One can reduce the vertical size; the scaling of the horizontal line will not be noticeable.

\documentclass{article}
\usepackage{amsmath,graphicx,bm}

\newcommand{\tsq}{%
  \text{\resizebox{!}{.8ex}{$\bm{\sqcup}$}}%
}

\begin{document}
$\tsq q_2\mathtt{0}$
\end{document}

With \bm the symbol will be blacker.

If you don't need the symbol in subscripts or superscripts, omit the \text around the main body.