Gas giant
The smallest known extrasolar planet that is likely a "gas planet" is Kepler-138d, which has the same mass as Earth but is 60% larger and therefore has a density that indicates a thick gas envelope.
Kepler-37b
To date, Kepler-37b is the smallest planet discovered around a main-sequence star outside the Solar System. Detection of Kepler-37b was possible due to its short orbital period, relative brightness, and low activity of its host star, allowing brightness data to average out quickly. The discovery of Kepler-37b has led Jack Lissauer, a scientist at NASA's Ames Research Center, to conjecture that "such little planets are common".