This can be done similarly to Biblatex: First citation as full reference and following citations ibid or - when interrupted - short author-year citation, but since your desired style is slightly different and you already have a lot of additional modifications, some care has to be taken.
I'd like to remark that usually when citations are identified with author-year labels, the year should have a more prominent place in the bibliography (and long citation), so that it can be found easily at first glance. With the current layout one has to search for the year near the end of the entry, while the name is at the beginning. Usually the bibliography would also be sorted by name-year for this citation set-up, but the MWE sorts by name-title.
The relevant modifications for this question in the MWE below are marked with https://tex.stackexchange.com/q/467022/35864. The other code as been collected from the many linked questions.
The main idea is to modify the cite:short macro to print labeldate instead of labeltitle. In order to use labeldate we need to request it with the labeldateparts option. The rest is pretty much straightforward if one copies some code from authoryear.cbx. We only need to make sure that the disambiguation letter also appears in the bibliography, hence the redefinition of the date macro.
\documentclass{article}
\usepackage[ngerman]{babel}
\usepackage{csquotes}
\usepackage[style=verbose, labeldateparts, autocite=footnote]{biblatex}
%%%%% https://tex.stackexchange.com/q/467022/35864
\newbibmacro*{cite:labeldate+extradate}{%
\iffieldundef{labelyear}
{\iffieldundef{label}
{\printtext[bibhyperref]{\printfield[citetitle]{labeltitle}}}
{\printtext[bibhyperref]{\printfield{label}}}}
{\printtext[bibhyperref]{\printlabeldateextra}}}
\renewbibmacro*{cite:short}{%
\ifbibmacroundef{cite:short:\strfield{entrytype}}
{\printnames{labelname}%
\setunit*{\printdelim{nametitledelim}}%
\usebibmacro{cite:labeldate+extradate}}
{\usebibmacro*{cite:short:\strfield{entrytype}}}}
\renewbibmacro*{date}{%
\iflabeldateisdate
{\printdateextra}
{\iffieldundef{extradate}
{}
{\PackageWarning{biblatex}{Nonempty 'extradate' in entry
\thefield{entrykey}, but labeldate is not date.}}%
\printdate}}
%%%%% 467022 END
%%%%% https://tex.stackexchange.com/q/466985/35864
\DeclareFieldFormat[online]{shorttitle}{\mkbibquote{#1\dots\isdot}}
\newbibmacro*{cite:short:online}{%
\printnames{labelname}%
\setunit{\addcomma\space}%
\printlist{organization}%
\setunit{\addcomma\space}%
\printdate
\setunit{\addcomma\space}%
\printtext[bibhyperlink]{%
\iffieldundef{shorttitle}
{\printfield[citetitle]{labeltitle}}
{\printfield{shorttitle}}}}
\DeclareSourcemap{
\maps[datatype=bibtex]{
\map[overwrite=false]{
\step[fieldsource=title, match=\regexp{\A(\w+\s+){2}(\w+)}, final]
\step[fieldset=shorttitle, origfieldval, final]
\step[fieldsource=shorttitle, match=\regexp{\A(\w+\s+)(\w+\s+)(\w+).*}, replace={$1$2$3}]
}
}
}
%%%%% 466985 END
%%%%% https://tex.stackexchange.com/q/464205/35864,
%%%%% https://tex.stackexchange.com/q/464166/35864
\DefineBibliographyStrings{english}{
urlseen = {visited at}
}
\DeclareFieldFormat{urldate}{\bibstring{urlseen}\space#1}
\DeclareListWrapperFormat{organization}{\mkbibemph{#1}}
\DeclareBibliographyDriver{online}{%
\usebibmacro{bibindex}%
\usebibmacro{begentry}%
\usebibmacro{author/editor+others/translator+others}%
\newunit\newblock
\printlist{organization}%
\newunit\newblock
\usebibmacro{date}%
\newunit\newblock
\usebibmacro{title}%
\newunit
\printlist{language}%
\newunit\newblock
\usebibmacro{byauthor}%
\newunit\newblock
\usebibmacro{byeditor+others}%
\newunit\newblock
\printfield{version}%
\newunit
\printfield{note}%
\newunit\newblock
\iftoggle{bbx:eprint}
{\usebibmacro{eprint}}
{}%
\newunit\newblock
\usebibmacro{url+urldate}%
\newunit\newblock
\usebibmacro{addendum+pubstate}%
\setunit{\bibpagerefpunct}\newblock
\usebibmacro{pageref}%
\newunit\newblock
\iftoggle{bbx:related}
{\usebibmacro{related:init}%
\usebibmacro{related}}
{}%
\usebibmacro{finentry}}
%%%% 464205 & 464166 END
%%%%% https://tex.stackexchange.com/q/464911/35864
\DeclareSortingTemplate{nty}{
\sort{
\field{presort}
}
\sort[final]{
\field{sortkey}
}
\sort{
\field{sortname}
\field{author}
\field{editor}
\field{translator}
\field{organization}
\field{sorttitle}
\field{title}
}
\sort{
\field{sorttitle}
\field{title}
}
\sort{
\field{sortyear}
\field{year}
}
\sort{
\field{volume}
\literal{0}
}
}
%%%%% 464911 END
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@Article{article,
author = {Hans Zimmer},
title = {Minimal music},
journal = {Some journal},
year = {2013},
number = {12},
pages = {40-41},
}
@book{book,
author = {Peter Babington},
title = {The title of the work},
year = 1993,
}
@incollection{incollection,
author = {Peter Farindon},
title = {The title of the work},
booktitle = {The title of the book},
publisher = {The name of the publisher},
year = 1993,
pages = {10},
}
@online{gates,
author = {Bill Gates},
title = {Save the world!},
date = {2016-05-04},
url = {https://www.gatesfoundation.org/de/},
urldate = {2018-12-04},
organization = {Bill {and} Melinda Gates Foundation},
}
\end{filecontents}
\addbibresource{\jobname.bib}
\addbibresource{biblatex-examples.bib}
\begin{document}
Lorem\autocite{article} ipsum\autocite{incollection} dolor\autocite{book}
sit\autocite{article} amet\autocite{incollection} concesctur\autocite{book}
aut\autocite{gates} lorem\autocite{gates}.
Lorem\autocite{knuth:ct:b} ipsum\autocite{knuth:ct:c}
dolor\autocite{knuth:ct:b} sit\autocite{knuth:ct:c}.
\printbibliography
\end{document}
verbosestyle with author-year short citations, but in that case it would be more natural to also use theauthoryearbibliography layout and sort references by name-year and not by name-title. Care would have to be taken for works by the same author from the same year. Usually in author-year styles they would be disambiguated with a little letter: Smith 1990a, Smith 1990b. But how should that letter show in the first citation? You also mention that this treatment should only apply to@article,@bookand@incollection. What about the rest? – moewe Dec 22 '18 at 19:55authoryearshort citations withstyle=verbose-ibid. – moewe Dec 22 '18 at 20:01bibstyle=authortitle(as this has a problem with e.g.articlein=false). I can test tomorrow which part exactely causes the problem and then add it to the MWE if this is of any help. – heidil Dec 23 '18 at 02:56@electronicI don't have any other bibliography classes. There the citation looks like [https://tex.stackexchange.com/questions/466985/change-to-a-shorter-citation-style-in-biblatex] I added some code with regard how the organization is displayed from other questions. If it's unnecesary for this question feel free to delet it again. (and if you already pointed out in another question some of the authors are in the same course, which explains the similar code.) – heidil Dec 23 '18 at 10:11