How do I get rid of ants on the water filter of our fridge?

One thing you can do is call the hotline of the manufacturer of your reftig. Have the make and model numbers ready. They can help you.

The ants have to be coming from somewhere either in the system or from the outside crawling up into the fill spout.

Have you checked the filter? That might be a possible entry if is not in tightly.

Please write back with your solution to your intriguing question

try to see if there is a source of sugar around. this is what is attracting them

Find where ants are coming in the home, find the trail and then here is an easy, inexpensive and SAFE way to kill the intruders. If you can, locate the mound under the house or near the foundation too. https://www.hometalk.com/diy/outdoor/pest-repeller/ants-safe-and-effective-cure-36651130 Photo by Jared Belson.

Ants come looking for water.... You could put a line of diatomecous earth or borax around the frig, I would also put a few drops of alcohol in the intake value with an eye dropper.

I'd turn the water off to the refrigerator until the ants are taken care of because eeeuuuuwwww! A 50/50 mix of Borax and table sugar is deadly to ants in 4 ways: kills them by piercing their exoskeleton, poisons the trail, poisons those who eat it, kills the nursery because they feed their dead to the babies = the Queen leaves!

If you've got pets as I do, I put it in Chinese take-out containers w/ tiny holes around the bottom.

Have you tried a bait trap? https://www.hometalk.com/diy/outdoor/pest-repeller/quick-dyi-sweet-bait-to-treat-and-get-rid-of-your-ants-18515410