The Japanese site Image no-mania (a sensor guru blog) thinks A9 sensor is nearly the same used by the new VENICE camcorder. That means the α9 sensor potentially can do 4k60fps or 6k24fps. If (again a big if) the new A7sIII (or a9s) has this sensor we can expect it to record 4k 60fps.
Note: Before you start saying that the A9 video features have been crippled down by Sony. While the sensor might be capable of 4K60fps you would need the processor to be designed to be a video workhorse. And you have to design the body in a way to avoid quick overheating.
Join the new Sony A7sIII facebook group.