Tuesday is the third day of the Human week.
The senior staff of the USS Enterprise-D held a weekly poker game every Tuesday evening. (TNG: "Cause and Effect")
A holographic Sigmund Freud wanted to give Data an appointment for "next Tuesday". (TNG: "Phantasms")
Several pieces of essential equipment aboard the USS Enterprise-B, including its tractor beam and photon torpedoes, along with the ship's medical staff, were scheduled for delivery the Tuesday after its maiden voyage. (Star Trek Generations)
On Tuesday nights, Jadzia Dax and Quark enjoyed a weekly game of tongo. (DS9: "Meridian")
Until 2372, Odo used to have meetings with Major Kira Nerys on Tuesday mornings in which they discussed the weekly criminal activity report. (DS9: "Crossfire")