Setiing Institute Logo

I see from your MWE that maketitle fills the whole frame, so instead I created the macro university just to format the institute as a line of text. Without the overlap, the titlegraphic starts running into the title (bad maketitle design).

documentclass[11pt]{beamer}
    usetheme[progressbar=frametitle]{metropolis}
    setbeamertemplate{frame numbering}[fraction]
    setbeamercolor{progress bar}{fg=green,bg=blue}
    makeatletter
    setlength{metropolis@progressinheadfoot@linewidth}{3pt}
    makeatother
    usepackage{tikz}
    usetikzlibrary{calc}
    usepackage[utf8]{inputenc}
    usepackage[T1]{fontenc}
    usepackage{lmodern}
    usepackage{amsmath}
    usepackage{amsfonts}
    usepackage{amssymb}
    usepackage{graphicx}
    usepackage{wrapfig}
    usepackage{float}
    
    newcommand{university}{CENTRAL UNIVERSITY OF HIMACHAL PRADESH hfil
      raisebox{dimexpr 0.5htstrutbox-0.5dpstrutbox-0.5height}[0pt][0pt]% align centers and overlap
        {includegraphics[width=0.2linewidth]{example-image-a}}}
    
    
    
        author{Anshul Sharma}
    title{Symmetry in Quantum Mechanics}
    institute {university}
    titlegraphic{includegraphics[width=0.2linewidth]{example-image}}
    
    begin{document}
    
        begin{frame}[plain]
        maketitle
    end{frame}
    
    begin{frame}[t]
    frametitle{Contents}
    begin{itemize}huge
        item  Aim
        item Objectives
        item Apparatus
        item Theory
        item Experimental Setup
        item Observations
        item Results
        
    end{itemize}
    end{frame}
    end{document}

You can edit the first frame code as under-- this will give you a picture graphic on the right side of your university title -- you can shift the position by experimenting with (x,y) values in (5,0.6) -- in place of the graphic you can use your own

     begin{frame}[plain]
                    begin{tikzpicture}[remember picture, overlay]
                node[anchor=north east] at ($(current page.center)+(5,0.6)$){includegraphics[width=0.1linewidth, scale=0.1]{example-image}};
                end{tikzpicture}
            maketitle
    end{frame}