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What from are you using stock or custom
Stock though at this point (where the ongoing issues and old OS leave me expecting to buy a new phone in the near future) I guess I wouldn't mind risking it if it's not too hard.

If you're trying to connect the PS3 controller wirelessly, you have to be rooted. First, if you're rooted, you need to download a program on your computer called "Sixaxis Pair Tool" (should be able to Google it fairly easy.) Once you've got the program installed, connect your PS3 controller to your PC with your mini-USB cable. The pair tool should give you Bluetooth code (you will need this to pair it with your phone).
Open the Sixaxis app on your phone and put in the code you got from the pair tool on your PC and pair it up with your controller. If all went well, the controller indicator lights should be light on "1"and you should be good to go.
Reminder, if you're using a controller that you play on your PS3 you will have to physically reconnect via your charging cable to resync it to your PS3, likewise, you will have to use the Sixaxis pairing tool on your PC to sync it back to your phone whenever you want to use it again.
Hope this helped you and anyone else that was having problems with this. It should work on your Triumph.
Side note, if you can get an OTG cable, you won't have to worry about rooting your phone, just connect it to both your controller and USB port on your phone and you're good to go, hassle free.