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Is it possible to have a citation style by name and year in text and alphabetically ordered and numbered list at the end?

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To get you started, consider this example:

\documentclass[]{article}

\begin{filecontents}{\jobname.bib}
@inproceedings{paperA,
    booktitle = {Proceedings},
    year = {2003},
    author = {Alpha, Author},
    title = {AAA Title of Paper},
}
@inproceedings{paperB,
    booktitle = {Proceedings},
    year = {2002},
    author = {Bravo, Author},
    title = {BBB Title of Paper},
}
@inproceedings{paperC,
    booktitle = {Proceedings},
    year = {2004},
    author = {Charlie, Author},
    title = {CCC Title of Paper},
}
@inproceedings{paperD,
    booktitle = {Proceedings},
    year = {2001},
    author = {Bravo, Author},
    title = {DDD Title of Paper},
}
@inproceedings{paperE,
    booktitle = {Proceedings},
    year = {2001},
    author = {Bravo, Author},
    title = {BEE Title of Paper},
}
\end{filecontents}

\usepackage[backend=biber,sorting=nyt,style=authoryear]{biblatex}
\addbibresource{\jobname}

% Make numbered
\defbibenvironment{bibliography}
{\enumerate{}
{\setlength{\leftmargin}{\bibhang}%
\setlength{\itemindent}{-\leftmargin}%
\setlength{\itemsep}{\bibitemsep}%
\setlength{\parsep}{\bibparsep}}}
{\endenumerate}
{\item}

\begin{document}

Text citation style:
\begin{itemize}
\item \cite{paperA}
\item \cite{paperB}
\item \cite{paperC}
\item \cite{paperD}
\item \cite{paperE}
\end{itemize}
\printbibliography

\end{document}

It provides the following style in text and bibliography:

bibliography

To move forward from here, consider the following resources:

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