It's called a wicket door, according to both the American Heritage Dictionary and Wikipedia. You can also Google it and find numerous image examples.
The Door.
The eye of a needle.
trap door
The door can be described as ajar.
next door neighbours
guarantee
eer
Yes, I LOVED them.
310 Pages.
A knock at the door is not an emergency. Try this: "Who is it?"
In Hindi, a door is called "दरवाज़ा" (darwaza).
I would call that the door jam area.