The less the access to the basement doors looks like a funnel the better it will function.

A sure fire fix is to locate some double doors at the top of the steps and add a roof and walls.

Or a drain at the bottom connected to the house's sewer system. (The red dot.)

Ditto.

The water is coming in under the door? Is the door flush with the surfaces inside and outside? It should at least be higher than the outside surface. Is there a drain at the bottom of the ”pit”? There should be!

Thanks for your comments. There’s no drain at the bottom. After heavy rain, there are puddles in the basement I’m not sure where it’s coming from but there’s a big puddle next to the basement door so I’m assuming it’s leaking from the door. It sounds like we def need to add a drain and maybe roof above.

Definitely a drain! The roof will help a little but a lot of water just flows down the steps. In addition to a drain at the bottom you will want to add a system that channels water away from the house and from the steps so less goes down there in the first place. Do you live where it gets cold in winter? Do the steps get icy?

Yes we live in MA so it snows and gets pretty cold in the winter, my contractor says with regular doors it will warp so also looking into external doors which will withstand the weather.

" my contractor says with regular doors it will warp so also looking into external doors which will withstand the weather. "

That does not make any sense. Regular Exterior doors will not "warp". That is an exterior application and must be exterior doors. I would use steel or fiberglass, not wood and most all (steel & fiberglass as well have a wood or a wood composite frame. The doors are only so good however, they will not withstand water that would flood the doors. That is why in my first reply I mentioned water management. You need to stop the majority of the water from getting into the stairwell and off the doors. Doors alone will NOT solve your issue.

There are flood doors and barriers.

FYI, that's not a walkout basement. It's a window well that someone inappropriately installed a door in.

"Climb out basement"?

We are all guessing since no photos have been posted.