This Minas Tirith, though maybe the lesser known, was actually the first, and may have been the namesake for that built later in Gondor.

It was a great watchtower, built upon Tol Sirion, by Finrod Felagund, in the midst of the River Sirion, to guard that pass there.

"Finrod held the Sirion, and upon the Isle of Tol Sirion in the midst of the river he built a mighty watch-tower, Minas Tirith; but after Nargothrond was made he commited that fortress mostly to the keeping of Orodreth his brother." - The Silmarilion, p. 143, Of Beleriand and it's Realms.

Orodreth held the great tower, until it was captured by Sauron late in the First Age.

**Additional information provided by ash_nazg4321.**
Encyclopedia entry originally written by Nienna-of-the-Valar