If it's a class AB amp, by definition it doesn't operate in class B.
If output transistors were perfectly linear, a class B push-pull amp would work without crossover distortion because the output devices would "hand off" the signal from one to the other without a gap. Unfortunately there's no such thing as a perfectly linear output device, so crossover distortion occurs in a class B amp when one output device stops conducting before the other one starts conducting. Class AB was introduced back in the tube era to bias both devices on around the point where the signal handoff occurs. The technique was well known by the late 1930s and is discussed quite thoroughly in Frederick Terman's Radio Engineering and Fundamentals of Radio, two classic engineering texts from that era.
There have been a few Class B solid-state audio amps. The Dynaco Stereo 120 and Stereo 80 were both Class B designs that relied on feedback to smooth out the crossover notch, and some other designs from the 1960s followed a similar design philosophy.