The authors must be separated with an and and not with commas or semicolons regardless of the expected output in the bibliography. See How to properly write multiple authors in bibtex file?. So
author = {Mueller, Thomas and Peter Mueller and Klaus Mueller and Maier Herbert},
would be correct.
You may want to consider using natdin instead of dinat. natdin is from 2006, while dinat is from 2000. l2tabu for example advises natdin over dinat. I would normally suggest biblatex and Biber nowadays (but then I may be biased).
Both styles write "u. a." instead of "et al." and both styles have facilities to change this, but in both cases that means you have to edit a copy of the .bst style.
The general strategy is the same
Locate the style you want to change on your machine. You can find the file path by typing kpsewhich dinat.bst or kspewhich natdin.bst into a terminal. Failing that get the files from CTAN: https://ctan.org/tex-archive/biblio/bibtex/contrib/german/dinat or https://ctan.org/tex-archive/biblio/bibtex/contrib/german/din1505
Copy the file to a place where LaTeX can find it (https://texfaq.org/FAQ-inst-wlcf), the directory of your current document will do just fine, and rename it. You must rename the file if you modify it, this is part of the license. Let's say the new names are dinat-etal.bst and natdin-etal.bst
Open dinat-etal.bst and go to line 122
FUNCTION {push.ua} { "u.\,a." }
replace it with
FUNCTION {push.ua} { "et~al." }
Open natdin-etal.bst, go to line 188 and replace
FUNCTION { ua.etal } { " u.\,a." }
with
FUNCTION { ua.etal } { " et~al." }
If you want to you can also change the string for and from "u." to "und" in the next line.
Save the file.
Use \bibliographystyle{dinat-etal} instead of \bibliographystyle{dinat} and \bibliographystyle{natdin-etal} instead of \bibliographystyle{natdin}.
You will want to use \citep and not \citep* to obtain a short "et al." citation. The starred version will try to print the full author list, thus suppressing any "et al.".
You probably also want to load natbib with the square option.
Use a package like tocbibind or a class option (KOMA) to get the bibliography to the TOC, don't add it manually with \addcontentsline.
\documentclass[12pt]{article}
\usepackage{lmodern}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{tocbibind}
\usepackage[square]{natbib}
\bibliographystyle{natdin-etal}
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@Article{Mueller2018,
author = {Mueller, Thomas and Peter Mueller and Klaus Mueller and Maier Herbert},
title = {On the testing of natbib},
journal = {my personal journal},
year = {2018},
}
\end{filecontents}
\begin{document}
This is a citation \citep{Mueller2018}
\bibliography{\jobname}
\end{document}
![This is a citation [Mueller et al., 2018]//References//[Mueller et al. 2018] Mueller, Thomas ; Mueller, Peter ; Mueller, Klaus ; Herbert, Maier: On the testing of natbib. In: my personal journal (2018)](../../images/4f83338ca5bd84a32f442513327c4fbe.webp)
andand not with commas or semicolons in the.bibfile, see https://tex.stackexchange.com/q/36396/35864. Soauthor = {Mueller, Thomas and Peter Mueller and Klaus Mueller and Maier Herbert},would be correct. It's too late for me to investigate the "et al." issue. – moewe Sep 12 '18 at 19:55and. After correcting this, your mwe produces(Mueller, Mueller, Mueller und Herbert, 2018)for citation,[Mueller u.a. 2018]for label, andMueller, Thomas ; Mueller, Peter ; Mueller, Klaus ; Herbert, Maierfor author names in the bibliography. Where do you want anet alto show up? – Zeping Lee Sep 13 '18 at 01:36