Yes, Shia Muslims do fast, particularly during the month of Ramadan.
While the general practice of fasting is the same between Sunni and Shia Muslims (abstaining from food and drink from dawn until sunset), there are some differences in the specific timing of breaking the fast. According to provided reference, while Sunni Muslims break their fast at sunset when the sun is no longer visible but there is still light in the sky, Shia Muslims wait to break their fast until it is completely dark after sunset.
