Standard shoulder presses get the shoulders strong in one plane, but a slight angular shift in pressing can make the mid or lateral delts work much harder.
To do the Y press, it's important to remember your angles. As you can see in the video, start with the palms facing each other at shoulder-width. As you extend the arms, the hands travel farther away from each other, and the fists rotate so that the palms face forward by the end.
You feel the most tension at the top, where the lever arms are the longest, which is why pausing at the top of each rep for a 1-2 second count is smart. It's also important that the arms don't drift too far in front of, or behind, the body. Keeping them in line with the rest of the body is key.
Lastly, note that the dumbbells are held with an emphasis towards the "near side" of the handle. That deepens the force angle at the top of the lift and can make light weight feel heavier. In the video, I'm using 20-pound dumbbells. When aiming for higher reps, it shouldn't take much more than this.
Y presses serve as an excellent accessory movement to follow barbell or dumbbell overhead presses.