\documentclass[tikz]{standalone}

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

\begin{tikzpicture}[scale = 2]

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

%draw exterior boundaries
\draw[out=30,in=-30,looseness=1.5] (0,0.3) to (0,1.5);
\draw[out=150,in=-150,looseness=1.5] (0,0.3) to (0,1.5);

%add pending arc
\draw[in=0,out=45,looseness =1.25] (0,0.3) to (0,1.3);
\draw[in=180,out=135,looseness=1.25] (0,0.3) to (0,1.3);

%draw crossing arc
%\draw[orange, thick,out=100,in=180,looseness = 1] (0,0) to (0,1.15);
\draw[orange,thick,in=165,out=0] (-0.5,1.2) to (0,1.15);
\draw[orange, thick,out=-15,in=0,looseness = 2] (0,1.15) to (0,0.8);
\draw[orange,thick,out=180,in=180,->=0.5,looseness=1.5] (0,1.2) to (0,0.8);
\draw[orange,thick,out=0,in=10,looseness=1.4] (0,1.2) to (0.1,0.7);
\draw[orange,thick] (0.1,0.7) to (-0.5,0.6);

%draw vertices and orbifold point
\draw[fill=black] (0,0.3) circle [radius=2pt];
\draw[fill=black] (0,1.5) circle [radius=2pt];
\draw[thick] (0,1) node {$\mathbf{\times}$};

%adding edge labels
\node[scale=0.8] at (-0.26,1.4) {$\alpha$};
\node[scale=0.8] at (0.26,1.41) {$\beta$};
\node[scale=0.8] at (0,1.36) {$\rho$};

\end{tikzpicture}
\end{document}