how to resize horizontally a screen region

At least on Debian and Ubuntu, the resize command, when applied to a full height region performs a horizontal resizing.

If it works for you, then first split vertically, next perform a resizing of the width, then split horizontally.

You can simply use resize command intuitively. Just type C-a : resize +10 to increase size and you can use -10 as well. You can use the same command for both vertical and horizontal window resizing

From the screen manual:

Command:

resize [-h|-v|-b|-l|-p] [ [+|-]n[%] | = | max | min | _ | 0 ]

Resize the current region. The space will be removed from or added to the surrounding regions depending on the order of the splits. The available options for resizing are

• -h (horizontal)
• -v (vertical)
• -b (both)
• -l (local to layer), and
• -p (perpendicular).

So C-a :resize -h 10 should work.