Your problem sounds like you may have a broken valve spring or a valve that is not seating due to damage.
Do a cylinder balance test on the engine to pinpoint the exact cylinder.Air the cylinder & make sure it holds pressure.if necessary remove the valve springs & inspect.look very closely at the valve guide to valve stem clearance .If you can move the valve side to side the guide is worn out.
The timing light will show you a problem "IF" the timing is moving caused from a fault.
Tr to find out which cylinder is backfiring through the throttle body before removing the springs.Do not mix up the springs.
You will need a special tool & a torque wrench to test the pressure it takes to depress each valve spring.If you do not have these tools I suggest you find the cylinder that is causing this problem ,remove the springs & replace if necessary.