Any other type of air filter by itself will have no affect on mileage whatsoever.
The only way to gain mileage is to get colder air than the oem intake air.
So if you buy a cold air intake (comes with filter) and you are drawng in cooler air than stock due to poor oem intake design, then your mileage and power may see a slight increase.
This works due to the timing/temp tune table in the PCM. The colder the air the more timing you can get, which gets you more torque for less throttle.