Beamer - specify logo position in title page

The position of the title graphics is determined by the theme. In this case it seems to be placed in the top left side of the slide. A quick (and a bit hacky) way to move it is to put it in a picture environment with zero width and height, and then place it where ever you like.

\documentclass{beamer}
\usetheme[sectionpage=none, progressbar=frametitle, numbering=fraction]{metropolis}        % Use metropolis theme  
\title{Title}
\date{\today}
\author{Author}
\institute{Title}

% logo of my university
\titlegraphic{%
  \begin{picture}(0,0)
    \put(305,-120){\makebox(0,0)[rt]{\includegraphics[width=2cm]{example-image}}}
  \end{picture}}
\AtBeginSection[]{
\begin{frame}{Talk Overview}
\tableofcontents[currentsection]
\end{frame}
\frame{\sectionpage}
}

\begin{document}
\maketitle
\end{document}

Play with the argument for \put to get it where you like.

Dirty but quick hack: Move the logo right with \flushright and down with \vspace:

\documentclass{beamer}
\usetheme[sectionpage=none, progressbar=frametitle, numbering=fraction]{metropolis}
\title{Title}
\date{\today}
\author{Author}
\institute{Title}

% logo of my university
\titlegraphic{\vspace{4cm}\flushright\includegraphics[width=2cm,height=2cm]{example-image-a}} 

\begin{document}
\maketitle
\end{document}

Just as an idea for future users (but don't accept it as an answers) you can always define your own titleframe and use it as you wish:

\documentclass{beamer}
\usetheme[sectionpage=none, progressbar=frametitle, numbering=fraction]{metropolis}        % Use metropolis theme
\usepackage{tikz}


\let\oldtitle\title
\let\oldinstitute\institute
\let\oldauthor\author
\let\olddate\date
\makeatletter
\def\title#1{\xdef\@title{#1}\oldtitle{#1}}
\def\author#1{\xdef\@author{#1}\oldauthor{#1}}
\def\institute#1{\xdef\@institute{#1}\oldinstitute{#1}}
\makeatother

\title{Title}
\date{\today}
\author{Author}
\institute{Title}

\makeatletter
\def\ttlframe{
  \begin{frame}[plain]
    \begin{tikzpicture}
      \node[anchor=west] at (0,-1) {\LARGE\bfseries\@title};

      \draw[orange,thick] (0,-2)--(\textwidth,-2);

      \node[anchor=west] at (0,-3){\@author};
      \node[anchor=west] at (0,-4){\@date};
      \node[anchor=west] at (0,-5){\small\@institute};
      \node[anchor=east,yshift=-0.3cm] at (\textwidth,-4) {\includegraphics[width=2cm]{example-image-a}};
    \end{tikzpicture}
  \end{frame}
}
\makeatother
% logo of my university
%\titlegraphic{\includegraphics[width=2cm]{img/politologo.png}} 

\AtBeginSection[]{
\begin{frame}{Talk Overview}
\tableofcontents[currentsection]
\end{frame}
\frame{\sectionpage}
}

\begin{document}
\ttlframe
\end{document}

PS: This gives much more flexibility in any case... but the existing answers are closer to the specific question solution.

PS2: The yshift just shows that you can adjust positioning and I wouldn't really use it.