Pictures might help, but in general, anything that could be broadly described as U-shaped, from a fountain to a gravy boat* needs a down-turned lip to prevent liquid preferring to adhere to the outside edge.
On these fabulously hand-drawn 'bowls', each design to the right will provide a better pour. The one to the far right has a lip that is lower than any other point, so the water has no choice but to fall, so long as the brown-coloured area is empty. Additionally, making a sharp edge will cause less adhesion.

If the fountain's cross-section looks like the right-most picture but the lip is filled like the brown insert, then hollowing it out to provide a proper break could work.
The 'perfect' edge would be more like this… lowest point and sharp.

The faster the water flows, the less it will adhere, but on this last shape, it will never climb back around the edge to pour down the outer surface.
I found a couple of examples from the interweb. The one on the left pours well, the one on the right probably doesn't.

* I don't know why, but it does seem to be an almost universal truth that all gravy boats are designed to pour gravy down the outer face of the boat & onto the table, rather than on your plate;) Now you know why. One day the gravy boat manufacturers may catch onto this idea.
After pictures added to question, and a little Photoshop magic to bring out the details…
The groove/channel marked in green needs to be cut deeper, so that the edge marked in red becomes sharper, more like my 'perfect edge' illustration above.
