Which historical order inspired the Templars in the Assassin's Creed series?

The Templars in the Assassin's Creed series are inspired by the historical Knights Templar.

The real Knights Templar were a Christian military order founded in the early twelfth century to protect pilgrims traveling to the Holy Land. They became wealthy and politically influential before being suppressed in the early fourteenth century.

The games reinterpret the order as a secret organization seeking control and stability through powerful artifacts called Pieces of Eden. Their ideological conflict with the Assassins drives the series across many historical periods, even though the fictional Templars and their goals are not a literal account of medieval history.

The Knights Hospitaller and Teutonic Knights were also real medieval military orders, which makes them understandable alternatives. However, the franchise's central antagonistic organization is explicitly derived from the Knights Templar, not those other orders.