\documentclass[tikz]{standalone}

\usetikzlibrary{decorations.pathreplacing,decorations.markings}
\usetikzlibrary{patterns}

\standaloneconfig{margin=12pt}

\begin{document}

\begin{tikzpicture}

% sets up command for arrows in the middle of arcs
\tikzset{->-/.style={decoration={
  markings,
  mark=at position #1 with {\arrow{>}}},postaction={decorate}}}

%draw vertices and orbifold point
\draw[fill=black] (0,0) circle [radius=2pt];
\draw[thick] (0.5,1) node {$\mathbf{\times}$};
\draw[thick] (-0.5,1) node {$\mathbf{\times}$};

%draw pending and exterior arcs
\draw (0,0) to node[midway,right,scale=0.75]{$2$} (0.5,1);
\draw (0,0) to node[midway,left,scale=0.75,yshift=3pt,xshift=1pt]{$1$} (-0.5,1);
\draw[in=0,out=0,looseness =1.75] (0,0) to (0,1.6);
\draw[in=180,out=180,looseness=1.75] (0,0) to (0,1.6);
\node[above,scale=0.6,yshift=-1pt] at (0,1.6) {$a$};

%draw gamma
\draw[orange,thick,out=90,in=90,->-=0.5] (-0.7,1) to (0.7,1);
\draw[orange,thick,out=-90,in=180] (-0.7,1) to (0.3,0.2);
\draw[orange,thick,out=-90,in=0] (0.7,1) to (0,0.8);

\end{tikzpicture}

\end{document}