Perhaps the smallest sundial goes to IBM with the printing of a sundial in a corner of a computer chip.  However it lacked a gnomon and could not really tell the time.  However, Chen Fong-shean, a Taiwanese miniature craftsman, was challenged by the French astronomical society to beat the Guiness World Record for smallest sundial held by an Italian.  The Italian dial created in 1999 measured 6.5mm x 5mm.

After failing a number of times Chen succeeded, carving a sundial on a grain of rice and setting a new world record of 5mm x 3mm.  Reported in the Taipei Times, https://www.taipeitimes.com/News/taiwan/archives/2022/05/26/2003778833 "Chen said that the secret of making a sundial out of a rice grain lies in securing the position of the grain during the process. He used tools such as a steel needle and writing brush to write tiny Arabic numbers from 6 to 18, covering the period between sunrise and sunset. Chen said that with the help of a magnifying glass, he wrote the numbers and drew lines on the sundial while holding his breath. The spacing of each number had to be carefully arranged since the rice grain was so small, he added. Chen said he found the work meaningful because it was an act of people-to-people diplomacy."