A Bronx 3-year-old is lucky to be alive and recovering at a hospital after falling out of her apartment window, her relieved dad said.

Kaddijatou Darboe climbed through the window and fell from the second-story of her family’s Sherif S. Byrd Place apartment Saturday night after moving a vinyl flap that held a window-unit air-conditioner in place, according to dad Sajor Darboe.

“It was screwed in. I don’t know how she did that. She is so fast,” said the dad, who has had to take care of his four children by himself since his wife died of cancer of the liver in May.

“I was fixing the food for them to go to the babysitter. When I came to the living room, I don’t see her so I said where’s Kaddija? Then I see the opening in the window and I ran outside,” he told The Post.

Neighbor Cynthia Olivia says she comforted the ailing child until Sajor arrived.

“I heard her fall. I was in my kitchen and I heard a thump and a man said there was a child on the ground,” she told The Post.

Sajor says when he got outside he could hear his daughter “crying and saying ‘Daddy, Daddy, Daddy.’”

The girl was taken to Lincoln Hospital for a leg injury and then moved to Columbia Presbyterian, where she has been under anesthesia while doctors conduct brain scans and other tests.

“The doctors and nurses said she is fine but they are waiting the final results of the different tests,” the dad said. “I’m very sad, but I’m very thankful to God for keeping her.”

Sajor’s wife passed away in May, and he must care for Kaddijatou, the girl’s 6-year-old sister and twin infants who will be 2 years old in December, he said.

The 3-year-old is a handful, according to Abdul Ali, 30, who has been living with Sajor for the last month.

“She’s very hard to control with three other kids,” he told The Post. “It’s very difficult for [Sajor]. I’m not blaming the child but I’ve been living with him and she’s hard to control. If you move her from here to there. She goes back. You tell her to stop and she doesn’t listen.

“I don’t want to blame [Sajor] that much because it’s difficult sometimes.”

Police are still investigating the fall, according to officials.