its going to be powered by a 9 volt switching power supply which really puts out 9.4. as for the 8050, i dont know its what it is labeled as.You want 300-350mA; that eliminates 2N3904. PN2222 and 2N4401 can handle the current, but can they handle the power.
What is an 8050?
That circuit will only give a constant current if the voltage source is stable.