\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=1.5pt];
\draw [fill=black] (0,1.6) circle [radius=1.5pt];
\draw[thick] (0.5,1) node {$\mathbf{\times}$};
\draw[thick] (-0.5,0.6) node {$\mathbf{\times}$};

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

%draws gamma
\draw[thick,orange,out=0,in=180,->-=0.1] (-0.5,0.9) to (0.4,1.4);
\draw[thick,orange,out=180,in=180,looseness=2.25] (-0.5,0.9) to (-0.2,0.4);

\end{tikzpicture}

\end{document}