Question: ```
\documentclass{article}
\usepackage{amsmath}
\usepackage{array}
\usepackage{mathtools}
\begin{document}
\renewcommand{\arraystretch}{1.2}
\newcommand{\minus}{\scalebox{0.4}[1.0]{$-$}}
\[
\begin{bmatrix*}[r]
  0&  \minus\frac{1}{2} &\frac{1}{2} \\
  \minus\frac{1}{2}&  0&\minus\frac{1}{2}\\
  \frac{1}{2}&  \minus\frac{1}{2}&0
\end{bmatrix*}
\]
\end{document}

```

[![enter image description here](https://i.stack.imgur.com/1yvlc.png)](https://i.stack.imgur.com/1yvlc.png)

How to reduce the number “0” size to fit fraction "1/2"? (reduce height of "0" ?)

---

update sample

As below photo shows the proportion close to 1/3

[![enter image description here](https://i.stack.imgur.com/Ofr0I.jpg)](https://i.stack.imgur.com/Ofr0I.jpg)

Answer: 
The image which the OP posted looks like display style fractions `\dfrac` were used. As stated in my comment, shrinking the `0` in these situations is uncommon. Generally speaking, the various `Tex` engines and most trusted and well used packages have good typographic features by default.

```
\documentclass{article}
\usepackage{amsmath}
\usepackage{array}
\usepackage{mathtools,xfrac}
\begin{document}
\renewcommand{\arraystretch}{1.2}
\newcommand{\minus}{\scalebox{0.4}[1.0]{$-$}}
\[
\begin{bmatrix*}[r]
  0&  \minus\frac{1}{2} &\frac{1}{2} \\
  \minus\frac{1}{2}&  0&\minus\frac{1}{2}\\
  \frac{1}{2}&  \minus\frac{1}{2}&0
\end{bmatrix*}
\]

\[
\renewcommand{\arraystretch}{2.0}%You will see what happens if you do not use it. It is a local definition which does not affect the third matrix
\begin{bmatrix*}[r]
  0&  -\dfrac{1}{2} &\dfrac{1}{2} \\
  -\dfrac{1}{2}&  0&-\dfrac{1}{2}\\
  \dfrac{1}{2}&  -\dfrac{1}{2}&0
\end{bmatrix*}
\]

\[
\begin{bmatrix*}[r]
  0&  \sfrac{-1}{2} &\sfrac{1}{2} \\
  \sfrac{-1}{2}&  0&\sfrac{-1}{2}\\
  \sfrac{1}{2}&  \sfrac{-1}{2}&0
\end{bmatrix*}
\]
\end{document}

```

Top: original; middle: `\dfrac`; bottom: <https://ctan.org/pkg/xfrac>.

[![enter image description here](https://i.stack.imgur.com/cR3SI.png)](https://i.stack.imgur.com/cR3SI.png)
I would say that your sample actually suggests the opposite: "I want to preserve regular size even for numerators and denominators". Use `\dfrac` instead of `\frac`.

Also, why do you have special treatment for minus? Why the `-` isn't enough?

```
\documentclass{article}

\usepackage{amsmath}
\usepackage{array}
\usepackage{mathtools}

\begin{document}
\renewcommand{\arraystretch}{2}
\[
  \begin{bmatrix*}[r]
    0             &  -\dfrac{1}{2} & \dfrac{1}{2}  \\
    -\dfrac{1}{2} &  0             & -\dfrac{1}{2} \\
    \dfrac{1}{2}  &  -\dfrac{1}{2} & 0
  \end{bmatrix*}
\]
\end{document}

```

[![enter image description here](https://i.stack.imgur.com/QLU1E.png)](https://i.stack.imgur.com/QLU1E.png)