turn the gap into a reveal
Make a shallow saw kerf all around the box at the intersection/gap. This will conceal the gap and provide a feature line.
OR make the kerf a bit deeper and add/glue in a filler strip of a different color wood or plastic like guitar binding, and there are epoxy fillers you can add ground ceramic material like turquoise, or metal if that would work with the design.
The answer to your question will only be as detailed and specific as the question is detailed and specific. Good questions also include a sketch or a photo that illustrates your issue. (:< D)