
\documentclass[11pt]{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{authblk}
\makeatletter
\newcommand@contributions{These authors contributed equally to this work.\textsuperscript{1}\textsuperscript{,2}}
\renewcommand@maketitle{%
\newpage
\null
\vskip 2em%
\begin{center}%
\let \footnote \thanks
{\LARGE @title \par}%
\vskip 1.5em%
{\large
\lineskip .5em%
\begin{tabular}[t]{c}%
@author
\end{tabular}\par}%
\vskip 0.5em%
@contributions% % <----
\vskip 1.5em
{\large @date}%
\end{center}%
\par
\vskip 1.5em}
\makeatother
\title{Thermodynamic of black holes}
\author{Albert Einstein\textsuperscript{1}}
\author{Roger Penrose\textsuperscript{2}}
\author{Rabindranath Tagore\textsuperscript{3}}
\affil{\textsuperscript{1}Princeton, USA
\
\textsuperscript{2}Oxford, UK
\
\textsuperscript{3}Delhi, India
}
\affil{Correspondence: r.tagore@gmail.com}
\begin{document}
\maketitle
Text
\end{document}
This answer redefines \@maketitle using help from Werner's answer to How does \thanks work in LaTeX article class?. I didn't notice that you were manually adding the affiliations to the authors via $^1$ which simplifies it. You can change the distances between \maketitle entries by modifying \vskip values.
Also, I changed your superscript notion from $^1$ to \textsuperscript{1} which I prefer (I am not sure if it is essential but it is better then using math mode in-text I think?). Modify the values in \@contributions to change to other authors as you wish, hope this is helpful.
\vspacein\affilcommand :\affil[3]{Delhi, India \vspace{1em}}– Manuel Cart Feb 11 '23 at 09:26