A car, truck or other vehicle backfiring is usually not illegal in most states.
That is unless you modified the car to actually backfire as some people add modifications to their vehicle to make it purposely backfire which is then illegal in some states.
But if there is something wrong with your car causing it to backfire then that would likely not be illegal and you'd likely just get a warning if it is illegal in your area and be told to fix the problem with the vehicle backfiring.
I've had cars and trucks years ago that would backfire and never once did I get stopped by the police or ticketed or warned about the car or truck backfiring.
A engine backfire is an explosion in a combustion engine that occurs in the air intake system rather than inside the combustion chamber.
The backfire can be caused by too much fuel getting into the engine or caused by bad spark plugs, bad oxygen sensor, ignition timing being off, bad ignition coils etc.
You should really get the vehicle checked out because backfiring could eventually lead to engine damage.