If by "deal with", you mean, were there any equivalents to window screens- I don't know that one. Before the germ theory of disease was accepted, "malaria", as the name implies, was thought to come not from flying insects like mosquitos but from some bad quality of the air itself, so perhaps not many would think a screen was useful, anyway- but that's rather speculative.

However, if by "dealing" you mean, controlling them, people were making fly traps. One kind was made of blown glass: here's a 19th c. version. Another used the common poisonous mushroom Amanita muscaria, placing it in sweetened water or milk, hence the common name "Fly Agaric". An actual recent scientific study found that the fungal toxin does not actually kill the flies but does make them inebriated, and so easier to swat.

https://www.sciencedirect.com/science/article/abs/pii/S0378874116302008?via%3Dihub