The middle dot of the mesh is outside the mesh itself as you can see in the shot below. Please let me know if I can recenter it or is there a workaround for this?
The ‘dot’ representing the face is positioned at the “centre” of all the vertices of that face - calculated as the average over all vertices. In your case you have a large ngon with many more than 4 vertices and the ‘average’ happens to be outside your mesh (drawn away due to all the vertices along the curve).
It isn’t a problem that the ‘centre’ of the face is outside the face itself but it might be a problem that the face is an ngon (more than 4 vertices) as it can cause problems further down the line (eg, when trying to animate or subdivide the mesh). It would be best to delete the face (X, Faces Only) and re-create it with better geometry (quads/tris).
The dot on a face simply shows the center of the face. Since your face is shaped in such a way that there is empty space at the center of the face, the dot appears outside the bounds of the face. This isn't a problem as it won't affect anything other than how the face is displayed in edit mode, and there is no way to move the dot. If it is an issue for you, the only way to get rid of it is to split the large face into smaller faces.