I want to emphasize the word "ANALOG" so that you understand that i am not referring to digital trigger buttons
I want to know what was the first controller with analog trigger buttons, not digital trigger buttons
Earliest I can think of is the 3D Control Pad for the Sega Saturn, released in July 1996. When the switch on the bottom face is set to O (for analog), the triggers (and directional pad) can be polled for analog values. When the switch is set to +, those inputs are polled for digital/binary values like on the stock Saturn pad.
The Namco NeGcon was released in 1995 and featured two analog face buttons as well as one analog shoulder button. Although it wasn't the official primary controller for the PlayStation, it was an officially licensed PlayStation controller.
The I and II buttons are both analogue and have approximately 7mm of travel, which can allow for sustained, responsive button presses. The buttons also detect how much the user pushes them. The L shoulder button is also analogue and has approximately 5mm of travel. All three analogue buttons have a rack driving pinions similar to the ones in the swivel-joint.
According to this list on wikipedia, the earliest controller listing analog triggers is the 1998 Dreamcast controller.