To create a halftone gradient in Krita, follow the following steps:
1: create a new vector layer. This is where we'll put our gradient. You can use a normal raster paint layer instead if you want to create the gradient using airbrushing, but let's learn how to do it with a vector layer first.
2: select the Rectangle tool in the toolbox.
3: draw a rectangle in the vector layer.
4: select the "Select Shapes" tool in the toolbox.
5: click on the rectangle that you drew to select it. In the Tool Options docker, you should see the properties of the rectangle, such as its position and dimensions, and a tab for the stroke settings, and a tab for the fill settings (with a bucket icon).
6: click on the bucket tab.
7: select gradient fill.
8: double click on the control points to edit their colors. Select a black to white gradient. It doesn't matter what color you want your effect to be, you'll always select black to white for this gradient.
9: adjust the position of the gradient by dragging the orange diamonds on the rectangle while the "Select Shapes" tool is activated.
10: add a filter mask to the vector layer. The filter that we want is the halftone filter.
Tip: to create a typical "growing circles (or bubbles)" pattern, select the Dots pattern and change Interpolation to Linear. You can switch whether the circles are white or black by checking Invert in the Postprocessing tab.
Tip: to make the pattern crispier, increase Hardness in the Postprocessing tab.
See How to Create a Halftone Effect in Krita for a complete tutorial.
11: add a second filter mask to the vector layer. This time we want a Gradient Map filter. Set the colors of the gradient map to the colors you want your halftone background pattern to be.
See How to Create a Duotone Effect in Krita for a full tutorial.
You should have created your halftone background effect. You can modify the gradient in the vector layer now and it will update automatically.
Alpha Halftone Method
The method above is great if you want to add a halftone to the background, however it isn't very useful if you want to cast a halftone on the foreground, over other layers. In this case, a technique that you can use is to use a gradient that fades to transparent and then change the Mode setting in the halftone filter from Intensity to Alpha. This will make the halftone effect apply to the alpha of the gradient instead of the color. Then you can use a clipping mask or fill the result with a single color to complete the effect.