Back in the days of yore (I mean: before biblatex) you had to concoct your own bst (bibliography style) file in pure BAFLL (BibTeX's Anonymous Forth Like Language) to process your bibliography with BibTeX, which was a pain, because... well, it was a FLL.
Fortunately, there is a nice little package called custom-bib which includes a nice little TeX program makebst to produce TeX batch files (dbj) to generate custom bst files trying to fulfill your expectations.
So, basically, you run
tex makebst
in your terminal, and the program leads you through an interactive interface, where you may select the options required to produce your style. At the end of the process, the program generates a dbj file, which is yet another TeX file you may run to produce the final bst file with your bibliographic style. This way, if you change your mind (of find out you fouled up), you may edit the dbj file, comment in/out the options of your choice, and produce yet another bst by running
tex yourstyle.dbj
You may still hack/kludge the final bst file a bit; but again, programming in pure BAFLL may be EXTREMELY PAINFUL if you are not used to it. makebst does a nice little job to jumpstart your task, and tweaking the byproducts is relatively easy.
Given the system's limits for answers, and following Alan Munn's advice in the comments, I am posting here a link to a first attempt to suit your needs: the batch file and generated bibliography style are posted on GitHub.
https://gist.github.com/jarnosz/931d6eb5ae1eef2c58407f8d3f9ec5ff
The bibliography style tries to implement what you ask for.
%-------------------------------------------------------------------
% This bibliography style file is intended for texts in ENGLISH
% This is a numerical citation style, and as such is standard LaTeX.
% It requires no extra package to interface to the main text.
% The form of the \bibitem entries is
% \bibitem{key}...
% Usage of \cite is as follows:
% \cite{key} ==>> [#]
% \cite[chap. 2]{key} ==>> [#, chap. 2]
% where # is a number determined by the ordering in the reference list.
% The order in the reference list is alphabetical by authors.
%---------------------------------------------------------------------
Just remember to declare your \bibliographystyle{plainad}: as the comment says, neither apacite.sty nor any other macro interface is required; so this bibstyle may work even in Plain TeX.
Here are the results:


apacitepackage andapacitebibliography style, allow authoryear-style citation call-outs only. – Mico Oct 12 '21 at 04:41If thats true, you might get off with using biblatex' numeric style and changing the order of the items as described here: https://tex.stackexchange.com/questions/12806/guidelines-for-customizing-biblatex-styles
– Michael Bölting Oct 18 '21 at 11:11\cite, it should display [1] and not the conventional APA format of (Author, Year). – M B Oct 18 '21 at 23:10biblatex. Want to keep it that way,bibtexonly? – jarnosc Oct 20 '21 at 21:59biblatex– M B Oct 21 '21 at 04:54[1] Kearon, C. et al. (1998). Noninvasive diagnosis... 128 (8): 633-677.AND a solution in EITHER pure bibtex OR biblatex. Correct? – jarnosc Oct 21 '21 at 05:41biblatexat all; at least for this particular job. – jarnosc Oct 22 '21 at 00:54