The following code seems to do what you are looking for. Since you're using a your own .bst file, you'd need to change that in the example and replace the demo .bib files with your own. It's much easier to do this with biblatex (see Adding numbers to Author Year citations in list of references for an example.)
\documentclass{article}
\usepackage{etoolbox}
\usepackage{natbib}
\usepackage{hyperref,url}
\newcounter{bibcount}
\makeatletter
\patchcmd{\@lbibitem}{\item[}{\item[\hfil\stepcounter{bibcount}{\thebibcount.}}{}{}
\setlength{\bibhang}{2\parindent}
\renewcommand\NAT@bibsetup%
[1]{\setlength{\leftmargin}{\bibhang}\setlength{\itemindent}{-\parindent}%
\setlength{\itemsep}{\bibsep}\setlength{\parsep}{\z@}}
\makeatother
\bibliographystyle{agsm}
\begin{document}
\cite{*}
\bibliography{%
/usr/local/texlive/2015/texmf-dist/doc/latex/latex-bib-ex/articles,/usr/local/texlive/2015/texmf-dist/doc/latex/latex-bib-ex/books}
\end{document}

\usepackage[numbers]{natbib}...? – Werner Feb 20 '16 at 00:04\usepackage[round]{natbib}. When I used\usepackage[numbers]{natbib}the citations in the text are changed to numbers, wheras references are OK. However I wants 'author-year' citations in the text. – Bartłomiej Stępień Feb 20 '16 at 00:29.bstand a minimal working example (MWE) that replicates the current behaiour? It would help greatly trying to solve your problem. – Werner Feb 20 '16 at 00:47biblatex; not so simple withnatbib. See How to get a numbered alphabetical bibliography with (author,year) citations for an example usingbiblatex. And an even simpler version here: Adding numbers to Author Year citations in list of references – Alan Munn Feb 20 '16 at 04:35