Explanation:

- The Tappa style of music is a unique form of North Indian classical music that was indeed refined and developed during the Mughal era.

- Option 1: Jahangir was a Mughal emperor known more for his love of art and culture than for specific musical contributions.

- Option 2: Shahjahan is often remembered for his architectural achievements, like the Taj Mahal, rather than developments in music.

- Option 3: Muhammad Shah is the correct answer. He was a great patron of the arts, including music, and it was during his reign that the Tappa style was significantly refined.

- Option 4: Akbar was renowned for his support of the arts and music but did not directly influence the Tappa style.