The output of a single entry is not enough to fully understand the bibliography style, so this can only be a start.
For future questions please note that you should run the MWE code you have provided in the question to make sure that it accurately reflects the status quo. There are several issues with the code as posted at the moment. It will definitely not run as-is.
Please also ask about one concrete aspect of the style you want to obtain per question. That makes your question easier to answer and more useful for future visitors. (Should I ask one question with many requirements instead of many questions on same topic?)
A number of aspects of the style will have been addressed elsewhere on this site, e.g. Suppress "In:" biblatex, Change ordering number and year biblatex, Biblatex article entry: volume (year), no. n like bibtex amsplain? (related also Biblatex: changing the order of entries), Remove Quotation Marks from Style. (I'm not saying these are easy to find, mind. Usually I only manage to find a suitable question if I know the answer and have an idea which bits of code to search for. But if you ask about one aspect per question, it is easier to find good Q&As where the issue is addressed.)
\documentclass[british]{article}
\usepackage[T1]{fontenc}
\usepackage{babel}
\usepackage{csquotes}
\usepackage[
backend=biber,
style=ext-alphabetic,
sorting=none,
maxnames=4,
minnames=3,
maxbibnames=99,
giveninits,
uniquename=init,
articlein=false,
]{biblatex}
\renewcommand*{\newunitpunct}{\addcomma\space}
\DeclareDelimAlias{finalnamedelim}{multinamedelim}
\DeclareFieldFormat[article]{title}{\mkbibemph{#1}}
\DeclareFieldFormat{journaltitle}{#1}
\renewbibmacro{journal+issuetitle}{%
\usebibmacro{journal}%
\setunit{\jourvoldelim}%
\iffieldundef{series}
{}
{\setunit*{\jourserdelim}%
\printfield{series}%
\setunit{\servoldelim}}%
\usebibmacro{volume+number+eid}%
\newunit}
\DeclareFieldFormat[article,periodical]{number}{\bibstring{number}~#1}
\renewbibmacro{volume+number+eid}{%
\printfield{volume}%
\setunit{\addspace}%
\usebibmacro{issue+date}%
\setunit{\addcolon\space}%
\usebibmacro{issue}%
\setunit{\addcomma\space}%
\printfield{number}%
\setunit{\bibeidpunct}%
\printfield{eid}}
\DeclareFieldFormat{pages}{#1}
\begin{filecontents}{\jobname.bib}
@article{Hochschild,
author = {Gerhard Hochschild},
title = {Representations of restricted Lie algebras of characteristic p},
journal = {Proceedings of the American Mathematical Society},
year = {1954},
volume = {5},
number = {4},
pages = {603--605}
}
\end{filecontents}
\addbibresource{\jobname.bib}
\addbibresource{biblatex-examples.bib}
\begin{document}
Lorem \autocite{sigfridsson,Hochschild}
\printbibliography
\end{document}
