Well that's an emergency level of ammonia. I would use at least a dose of Prime (or any other solution that neutralizes ammonia). It will still read 3 ppm on your scale but it will be neutralized. It's up to you but there is a solution called AmGuard that supposedly lowers the amount of ammonia in your tank. Instructions on the back. I only use it when I'm in a situation with high ammonia levels like you are - ie., emergency. I have never killed a fish, I've even used a full capful on a 5 gallon aquarium that had ammonia readings of 8 pmm. It dropped it to 3pmm so I added 1/2 capful the next day and it brought it down to 1 pmm. From then on I stopped using it. Problem has been for me with this tank is that eventually the ammonia creeps back up to 4 and then I have to use Prime,Stabilizer and AmGuard. This tank was never cycled but I needed it for an emergency situation. It's only killed 1 fish and that was because I dropped the lid on it and killed it - none of the chemicals appear to even cause any mild distress. I mix all chemicals with about a quart of tank water first to get them well distributed. I do think the AmGuard may be preventing it from cycling but I didn't know what else to do when I had readings of 8 ppm.
How was the tank cycled? With ammonia or with fish? 4 weeks to cycle is kind of fast (at least for me - mine are always about 6 weeks long). When you were done cycling did it show 0 ppm ammonia and 0 ppm nitrites for at least a couple days in a row? If so then you likely were cycled if not, then you stopped mid-cycle and that would explain the 3 ppm now. Do you believe your fish tank is over stocked with fish? (I didn't see the size of your tank mentioned, just that there weren't a lot of fish).
How often do you do a water change? Try weekly 76% Make sure to use Prime to neutralize the chlorine and ammonia (and if the ammonia reading is over 2.0 use AmGuard, otherwise just add Stability to try to get it to cycle. I had 3 tanks in this situation (2-29 gal and 1-5 gal). One of my 29 gallons is so close to being cycled, it should just be a few days. The other 29 tank I'm fight some with - I do a major water change and get my ammonia down to zero for a couple days then suddenly it jumps up to 4.0. Nitrites are running 1.0 ppm constantly. I get the ammonia down to 1 or2 again and again it spikes up. The problem here is that while I don't have a lot of fish in this tank, most are 6-8" fish and they are overcrowded so I think I'm fighting their excess waste as well as any wasted food (which is very rare). The 5 gallon won't even make an attempt to produce nitrites. The good news - I hope is that I have a 3rd 29gallon tank in the middle of cycling. The big fish will be split up between the 3 tanks, with "B" tank holding all the "semi-aggressive" fish (amazing there are some because they are all Gourami's) - the other two tanks will only have Peaceful large Gouramis (still very competitive but less persistent about it). At that point I'll remove all the fish from my 5 gallon tank and place them in a peaceful tank (they are very tiny) - then work on doing a proper cycle for it so I can have a betta (maybe) or a quarantine tank (I think it's too small for that) - or maybe some cool tiny pencil fish or 5 sparkling gouramis (semi-aggressive but small)
Sorry for the long response - I live alone so I talk a lot when I can LOL.