Just as you have a dominant hand, you also have a dominant eye. You need to aim with the dominant—or master—eye for the most accurate shooting. Usually your dominant eye is the same as your dominant hand, but not always.
To determine your dominant eye:
If you’re not sure, close one eye at a time. The weak eye will see the back of your hand; the strong one will be focused on the object in the triangle.
There are various ways to address cross dominance (ie. you are right handed, but your left eye is dominant or vice versa).
Use a patch on your glasses - when applied to the lens of the shooting glasses over the offending eye, this subtly prevents the eye from focusing, while maintaining depth perception and peripheral vision. See magic eye dots.
1. Use red dot sights. This allows one eye t acquire the target and the other acquire the red dot. The shooter’s brain superimposes the two, enabling precise aim. With cross-eye dominant shooters, the stronger eye looks at the target and the weaker eye picks up the red dot, leading to a sight picture as good as or superior to that of regular shooters.
2. Learn to shoot with your non-dominant hand, mounting the firearm on the same shoulder as your dominant eye. This will take some time.