As Scout ran by the Radley house one day after school, she spotted a shiny object in one of the Radley's oak trees. When she reached up to the knot-hole, she found two pieces of chewing gum wrapped in tinfoil. Later, she showed Jem where she had found the gum, and they discovered another tinfoil package waiting for them in the knot-hole. It was a small box lined in "purple velvet." Inside were "two scrubbed and polished pennies... Indian-heads." Next they found some string--"a ball of gray twine." On another visit, Jem and Scout found a pair of figurines--"almost perfect miniatures" of the two children. Then came an entire pack of gum and, later, a "tarnished medal" that proved to be an old spelling bee award. Finally came their "biggest prize": a pocket watch with a knife attached to a chain. It would be the children's final gift, since the knot-hole was soon filled with cement.
Scout finds several things in the knothole, as something new pops up every time she goes back to check on it. However, the first time she finds something is in chapter four, when she finds gum.
If you need to know other occasions where she finds something, you can take a look at the chapter summaries provided in the eNotes study guide. Chapters four, six, and seven mention the knothole. Here is the link: http://www.enotes.com/topics/to-kill-a-mockingbird/summary The chapter summaries can be found by expanding the "Summary and Analysis" title.