Is there anything to try or does the fill valve just need to be replaced?
A toilet with a floatless fill valve isn't fully closing and is filling past the overflow tube (blue circle in image):
I have adjusted the adjustment knob (red circle) as much as possible to lower the water level. If observed closely in the image, the diagram at the right of the valve indicates to turn clockwise to "raise" or counterclockwise to "lower" the water level. Turning it completely counterclockwise essentially closes the valve and causes the water not to fill at all or to fill very very slowly, however it does not seem to adjust the water level as much as I need.
To my recollection, even when this valve was brand new it was difficult to get the adjustment right. It brought the water level to the edge of the overflow tube, but over time it has gotten higher, at first barely seeping over the top, and now it's overflowing constantly.
Another thought was to try to add some extension to the overflow tube but that might be more trouble than it's worth.