I have a problem with my amp. Amp model is Ampeg BA-112. And the guitar is Fender 60 Classic Jazz Bass (Mexico). So the problem is when I turn up neck pickup it starts to hum. What could happen to be a problem?

How bad is the "hum". Because I suspect your amp is fine but the root cause is the Jazz bass. When the pickups on some jazz models aren't set to similar levels, you tend to get a hum, especially in the neck pickup.

The best recourse is to swap out the factory pickups for hum-cancelling pickups. Aguilar, Seymour Duncan, and Fralin amongst others make hum cancelling pickups for Jazz basses.
The problem is probably just the nature of the pickups. That's just what happens with single coil pickups. If it's bothersome, you could try looking for some noiseless pickups.

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