There are two types of ammonia remover.
Zeolite and similar products absorb ammonia removing it from the water. The problem is that the ammonia is no longer available to the bacteria in the tank so they never multiply to enough numbers to 'eat' this ammonia. And these products get full and stop absorbing ammonia. This ties you into changing the product before it gets full forever. Failure to change it in time results in another ammonia spike.
There are products that temporarily convert ammonia to a less toxic form, and are found in a lot of dechlorinators. The effect lasts about 24 hours which means water changes still need to be done every day, but at least the ammonia in the tank doesn't harm the fish as much. The 'detoxified' ammonia still shows up in our test kits.
Ammonia exists in 2 forms in our tanks, ammonia and the less toxic ammonium. The proportion in each form depends on the pH and temperature of the water. One thing you can do is enter your ammonia reading, pH and temperature in this
ammonia calculator (set salinity to zero) and click calculate. You want the lower figure, NH3 concentration. This figure should be kept under 0.02, though up to 0.05 is tolerable for a day or two.
Can I ask what the filter is, and more importantly, what media are inside it?
And when you say you did a fishless cycle, was that following the method on here by adding ammonia or just letting the tank run without fish?
And have you tested for nitrite? If your ammonia is spiking, nitrite could well spike as well, though that would occur shortly after the ammonia spike.
According the the Community Creator on here, your tank is not stocked to the limit, but your fish are not in big enough shoals. It is recommended to have at least 6 in a shoal, and tiger barbs are better with at least 10 of them to keep their nippy behaviour within their shoal. Unfortunately, a 60 litre tank is not big enough for so many tiger barbs.
I do wonder if your problem is either that your fishless cycle was just running the tank empty, or that there is something about the media in the filter, for example cartridges containing zeolite which have just become full. If you could let us know about these two points we'll be better able to advise.