Running the filter will not help clean the tank if the nitrogen cycle isn't set up and the filter isn't on continuously.
I have a 2.5 gallon tank, and I change the water 100% every 2-3 days, depending on how much frozen food/poo is on the bottom of the tank :P
Changing your water 100% frequently will do MUCH more good than turning the filter on and off. It will prevent illness and your fish will love you for the super clean tank! :)
If you would rather not clean your tank this often, here is a link to how to set up your aquarium cycle! :)