Filters are quite useful when attempting to cycle. However, for the size of your tank, cycling is something you really won't need to worry about.
As gnats said, remove the filter altogether. To keep the water clean and clear you will need to undertake a 50% mid-week water change, and a 100% end-week water change. The reason for this is ammonia (fish waste). Even if you left the filter running in the tank, ammonia would still be in the water until you changed it.
Ammonia will build up and once it reaches a certain level, it has the capability to poison and kill your fish. This is the #1 reason for fish dying. In larger tanks you can undertake less water changes and space them out. However because you have a smaller tank, it will be necessary to keep to the 2 WCs a week (water changes). Please factor this in as it may affect your schedule at work or free time.
I also recommend this for environments where lights are on all the time to minimise stress. Depending if your workplace turns the lights off at the end of each working day, you may need to create an artificial ‘night’ for him. This is as simple as placing a breathable dark cloth over the tank to create darkness for the time when you leave work to getting in the following day. The issue however is then weekends, fasting him over the weekend won’t negatively affect him in anyway, and my opinion is that it is better to leave them in a partially dark environment than exposed to 48 hours of artificial light. But again, this only really applies if lights are on at your workplace 24/7.
Have a read of the intro stickies which will assist you in any other basics and you should have one happy Betta!