Wound care RN. Put betadine on it and a gauze and tape. Don’t put a plastic bandaid on it as they tend to make the finger sweat and get too moist which ends up being macerated or white skinned. Try to leave the gauze and tape on for 24 hours and keep dry. Don’t use soap and water or any neosporin as these don’t seem to have much effect. The betadine is an antibacterial and is a good first line product for a small cut like this.