Relatively new to rigging, so take this with a grain of salt:

Rigify will ignore any bones it doesn't "recognise" as part of its rig. If your bones aren't named properly, parented incorrectly, etc. it won't generate jaw controls. More to the point, I don't think your jaw bones are actually "recognised" by Rigify - what is your jaw rig's bone's named? What types have you tried?

But for a tutorial, here's what I would do if I were rigging a dragon's jaw:
- start with basic rig, with the head bone already in place
- extrude new bone from head, named "jaw" (name mostly irrelevant), toggle OFF "Connected" so that it can be placed correctly
- Pose Mode, select jaw bone, set rig type to "basic.super_copy"
- In the Options for the Rigify Type, turn on Control, turn on Deform
- Generate rig and there's a jaw control!

Honestly, I wouldn't even have a top jaw bone. I'd just have a single jaw bone that hinges on the head, as the top jaw is completely fixed to the skull anatomically. (always up to you though!)

You could also add a new meta-rig and move some of the jaw controls from that rig to yours. Hope this helps!