It's a MK4 transmission (02J) with the earlier MK3 (02A) shifter linkage to be precise.
I converted my B4V to the later style 02J shifter, and would do so again in a heartbeat - I found it to be that much more precise.
Note, I also upgraded mine with the TT shifter "golf club" to shorten fore/aft throws (does nothing for side to side)
to convert yours, you would need the shift lever from inside the car and the attached cables, the cable retainer bracket from the top of the transmission, the cable ends, the "golf-club" weight from the top of the transmission and most importantly, the sector/shift shaft that goes down into the transmission. You may also need the vw emblem piece (bottom of the transmission) that the above sector shaft sits in.
These parts are not TDI specific - they can come from any manual 02J jetta or golf.
There are two styles of shifter end as well - pin end and ball-end. The pin end are more common for when you may need replacement parts. Parts can be sourced at almost any junkyard.
A conversion well worth it in my opinion, especially if you are able to do the labor yourself. Others think not.