What affect will the mist from insect foggers have on DNA in a room?

You will need to explain more clearly what you mean by "DNA in a room".

I think I get the general gist of what he's attempting to ask -

He may be asking about household insect pests (term used loosely to define any organism that can be categorized as a nuisance like cockroaches, ants, spiders, etc) and their ability to genetically encode resistance to the poisons/toxins in their progeny.