The writing of a story within a story is known as frame story.
Explanation:
Frame story is a narrative story, where the narrator writes or tells a story within a story to fulfill the goals of his plot, more like a supporting aspect to the main story.
The author's story about his first child is the main story and sharing a memory of his childhood story is the supporting frame story. Frame story is found in various parts of literature like in art, novels, movies, opera etc,. The writing of a story within a story is known as frame story.
