Not an answer.
I do not know the "alpha" style.
There is nothing special about xecyr: it just uses the usual Unicode-aware packages and compilation method.
xecyr works by using (1) the article documentclass: (2) the packages polyglossia, fontspec, and natbib; (3) a font with Cyrillic glyphs: (4) and compiling with xelatex.
See the file rubibtex-ex-x.tex in the xecyr document folder. (Do texdoc xecyr for documentation.)
Swapping over to package biblatex instead of natbib required changing 3 lines of code in a 7-codeline file.
So: mapping the changes to Hindi (and making Russian not the main language any more) gives:

I put a title= field in, to show its location, borrowed a Russian bibentry from another question for comparison, and arbitrarily selected an authortitle style (initials can be set via the package options - see the manual).
Biblatex also auto-detects language settings from polyglossia and from babel, so hard-coding font switching in is not required.
This can be used as the starting point of your question, if you like.
If you use bibtex with its lack of ability, you will quickly find (if I may call it so) a "plethora" of convolutions waiting to greet you.
Whichever process you chose as the optimal path to the solution for your requirements, either bibtex or biblatex, will depend on constraints that you have not (yet) surfaced to anyone in a position to help.
MWE
\begin{filecontents*}{\jobname.bib}
@book{ramanujan,
author = {श्रीनिवास ऱामानूजन},
title={no title},
series = {Notebooks},
volume = {4},
date = {1920},
langid={hindi},
hyphenation={hindi},
}
@book{Baranov2001,
address = {Санкт-Петербугр},
author = {Баранов, Николай А},
title = {{Эволюция взглядов}},
year = {2001},
langid={russian},
% hyphenation={russian},
}
\end{filecontents*}
\documentclass{article}
\usepackage{fontspec}
\setmainfont{Noto Serif}
\newfontfamily\hindifont{Shobhika}
\newfontfamily\russianfont{Noto Serif}
\usepackage{polyglossia}
\setdefaultlanguage{english}
\setotherlanguages{hindi, russian}
\usepackage[
style=ext-authortitle-ibid,
bibencoding=auto,
autolang=other,
language=auto,
]{biblatex}
\addbibresource{\jobname.bib}
\begin{document}
Text text \parencite[14]{ramanujan} and \parencite[pp 15-16]{Baranov2001}.
\printbibliography
\end{document}
{\relax ...}trick to manually give the correct initial, though, that should even work with BibTeX (it did work for me in https://gist.github.com/moewew/9fb8ec18d78cef3216088dba241e0e6d, but for lack of a proper MWE I didn't test that with your example). – moewe May 30 '20 at 17:37