So the weapon that was used against the fleeing transports when
Admiral Holdo used the hyperspace ramming to destroy Snoke's ship?
The weapon fired a green laser beam and it arched. What's the weapon called?
The film's official novelisation indicates that the Supremacy is armed with two gigantic turbo-laser cannons.
Veins of illumination ran along the kilometers of its surface to a central command area the size of a major metropolis. And it was armed with giant turbolaser cannons from bow to stern—on both sides.
There's a nice description of how normal turbo-lasers function here. Presumably the ones on Snoke's flagship are much the same, just scaled up.