The 4 phase oscillator is made from simple 4 Bjt-s ring counter. The oscillator needs a reset pulse with button (schematic) or transistor at beginning to generate a nice 4 pulses one by one, otherwise it will just switch between phases 1&3 and 2&4.
The driver is made from 4 N-ch mosfets. To avoid draining an excessive power the motor phases are driven with short pulses (not a permenent supplying) by using RC derivative (47k, 100n) in front of mosfets gates.
Here’s the motor is supplied with 8V together with logic (ring counter, gates) but connecting the motor phases to different voltage (like 12V) is also possible.
Don’t use voltage higher than about 8V (best is 6-8V) for supplying the ring counter otherwise an EB breakdowns can appear on Bjt-s.
Bjt-s I used in this project are BC547C (not a SMD types).