There's a single quest exclusive to the Trink in the current version of the mod, called 'Prime Circuit", which will reward you with the Trinkian-exclusive Unique weapon upon completion. In order to start the quest, you need to play as a Trink and take the Broken Prod from your ship locker. Complete the vanilla Glitch mission, then take the Broken Prod to any Trinkian settlement. There will be a large central computer offering you a quest to repair the weapon.

Originally posted by Denouement:

i cant find the recipe for trinkian mining laser, and im very confused.

The blueprint for the Trinkian Mining Laser is sold by some Trinkian merchants in their settlements, but only on higher difficulty planets (tundra, for example). Every Trinkian settlement on these planets should have at least one merchant selling weapons and blueprints!