Which Muslim factions during the Crusade used the crescent in their flags or banners?

Question

According to NSNoob comments on Did Hungarian Army ever use Crescent banners?

Crescent was used by Muslims since the Crusades.

Wikipedia seems to agree. For example: the article on Star and crescent says

The use of the crescent symbol (without the star) on Muslim flags is first seen by Europe during the Crusades.

Wikipedia further listed 14th century examples of flags with crescents: flags of Gabes, Tlemcen (Tilimsi), Damas and Lucania, Cairo, Mahdia, Tunis and Bud; blue ensign of Nubia/Dongola; yellow ensign of the Mamluks. But the Crusades in the Middle East was happening earlier, in 11th-13th century. Briefly looking at the major factions, seems like the Seljuk empire, the Abbasid and Fatimid caliphates and the Ayyubid sultanate don't have crescent in their banners.

Which Muslim factions included the crescent as flags/banners during the initial Crusades of the 11th-13th century? Those that included crescent-and-star are also acceptable.

Answer 1

Heraldry information on the Crescent claims(without source unfortunately):

...in some instances one can trace the introduction of the crescent in European heraldry to Crusaders returning home.

Follwing this information, I found one example of a faction recorded as present during the Siege of Damascus during the Second Crusade:

(according to Nicolle, David The Second Crusade, Osprey: London page 58:)

There was ferocious combat in the orchards and narrow roads between the Christian force and a mixture of professional troops of Damascus, the ahdath militia and Turkoman mercenaries.

also from Syrian chronicler Abu Shama(also from Nicolle book):

Despite the multitude of ahdath [militia], Turks, and common people of the town, volunteers and soldiers who had come from the provinces and had joined with them, the Muslims were overwhelmed by the enemy's numbers and were defeated by the infidels.

Both these statements confirm the presence of Turkish mercenaries fighting for Damascus. The Crescent symbol has been associated with the Turks:

In the 12th century the crescent and star were adopted by the Turks

as far back as the Gokturks :

...pre-Islamic Turkic nations such as the Göktürks used the crescent and star figure on their coins

So, with the presence of Turks at this battle, it follows that the heraldic usage of the crescent shows the encounter of that symbol during this battle at least. A good source on heraldry may be able to confirm actual nights who used this emblem , but that's probably a question all of its own!