What kit are you using to test the water?
Those readings are very odd. I wouldn't expect a nitrate reading of 0ppm ever, really, unless your tank is absolutely stuffed full of plants (to the extent that the fish can hardly move), although this could be a mis-test, if you are using the API kit.
I'm also a little confused by how come you are showing 0.3ppm nitrite. Most test kits, certainly those that I have used, go from 0.25 to 0.5, so can you clarify how you've got that figure, please. If you are showing nitrite, it could be that you have had a minicycle in the filter, which has re-established itself for the ammonia, and what you are seeing is the residual nitrite as the bacteria catch up.
Can you confirm how long the tank has been set up, how you originally cycled the filter, what size the tank is, what other fish are in there, and if you have added anything different or new (decor, livestock, chemicals, etc.) recently.