My jaguar s type 3.0 v6 have a bad rough hiddling and very hot steam from one of the exit exhaust pipe that happened after the rain what it can be? But I was suspected coils

A smoke test might be best.

You might first like to look at the fuel trim behaviour.

Also, inspect for air leaks.

If you have them, change the IMT valve O-rings.

My first guess would also be in the directions of coils and plugs but there may be some stored codes that could provide you with some more concrete pointers.

may be some stored codes that code provide you with some more concrete pointers.
Iong time fault code is p1637 the one after rain is p1647

P1637:

CAN Link ECM/ABS Control Module Circuit/Network

P1647:

Linear O2 Sensor Control Chip (Bank 2)

As a starting point I would check to make sure your battery is up to snuff and charging system is working properly; then check all chassis grounds for proper connectivity.

The oxygen sensor issue on bank two is most likely playing havoc on your fuel trims and this is contributing to the lack of normal performance, The fact that this happened after a rain suggests that water intrusion may be a factor in your problem.

You also did not indicate the model year of your car, or its VIN. The early and later cars have different electronic engine management systems.

I'd suggest flooding the hood and windshield with water from a garden hose for a few minutes. Then open the hood and see if water has collected anywhere. Sometimes rainwater will collect in the spark plug wells and cause rough running. In that case, the culprit is a worn seal where the hood meets the cowl.