This is based on the solution given in this question.
I'm using trad alpha, but I don't have year for two papers from the same author:
\documentclass{book}
\usepackage{filecontents}
\begin{filecontents}{chapterref.dbx}
\DeclareDatamodelFields[type=field,datatype=literal]{
shortdesc,
}
\DeclareDatamodelEntryfields{shortdesc}
\end{filecontents}
\usepackage[backref, refsegment=chapter, datamodel=chapterref,
style=trad-alpha % https://tex.stackexchange.com/a/69706/38244
]{biblatex}
\usepackage[colorlinks]{hyperref}
\begin{filecontents}{\jobname.bib}
@misc{A01,
author = {Author, A. and Duthor, D.},
year = {2001},
title = {Alpha},
shortdesc = {Conference1},
}
@misc{noyear,
author = {Nuthor, C.},
title = {New title},
}
@misc{noyear2,
author = {Nuthor, C},
title = {More new title},
}
\end{filecontents}
\addbibresource{\jobname.bib}
\begin{document}
\chapter{First Chapter}
Some more text \autocite{A01}. More citation \autocite{noyear} and again \autocite{noyear2}
\printbibliography
\end{document}
Notice that the citation keys are [Nuta] and [Nutb] (highlighted in yellow):

What I want is, The index for the same key is to be Arabic numbers (instead of alphabets) with an upper comma before it:
[Nut'1], [Nut'2]
How to achieve that?