If 680 ohms is to high, what value would I need to obtain the 3 Amps maximum current ?
If it was a 12V AC secondary transformer, so about 12 x root 2 - bridge diodes (about 2 volts ) = about 15V.
Min 2N3055 Hfe at around 3 Amps, is about 20 (4 amps in datasheet).
So 3V across that resistor (R1), needs to supply about (3000/20 =) 150 milliamps.
R = 3/0.15 = 20
BUT that would not work in practice (or more accurately, it WOULD work, but the zener/resistor would get really HOT!), because the peak current (at the top of the ripple voltage, and when no output current), would be about 10 volts (across R1, estimated NOT calculated, as I don't know what capacitors or AC voltage transformer you are going to be using).
Which would then be about 0.5 Amps.
So the Zener would have 0.5 x 12 = 6 Watts, which is rather high. (Because the ripple voltage goes up and down, the average dissipation would be less than 6 watts. But with no output load, it would be 6 watts (est), all the time).
So it is NOT a good circuit for using at higher currents, sorry.
But another option is to use a power darlington transistor (instead of the 2N3055, the darlingtons huge gain would mean it needs little current to turn it on) or use a better designed circuit.
N.B. Exact values, depend on the specific components you use, such as the transformers secondary, AC output voltage etc.
EDIT: Figures updates. I used 4 amps, instead of 3 amps, so original figures wrong. Now corrected.