Having aptasia is kind of like Kevin from Home Alone fighting the T-1000.
And yes... there's a gif for that!
Highly recommend removing the rock, but if its needed in your tank try covering the nem with expoxy.
If its trapped it will die, if the rock is porous enough it may relocate.
May the odds be ever in your favour.
A syringe and vinegar. Hit them right in the center and they whither and die. I was able to control mine once I found them. I had about 5 or 6 when I started treatment and they were gone after about 2-3 months of weekly injections to the new polyps
If you can, take the rock out and kill it. Use something that will murder that SOB before it can spread like the plague. burn it, bleach it, smash it, napalm it, do something! if you cant get the rock out then try mixing some kalk and squirting it on it in the tank with a syringe but be careful because kalk paste will burn corals if it comes in contact.
Good Luck and be vigilant. If you let 1 in the tank then before you know it you'll have dozens and be trying to find something that eats it or boiling your rock.
For me, it is almost impossible to completely eradicate them.
The best I can do is to control them by injecting them with Aiptasia X. This stuff doesn't completely kill it most of the time.
With a lot of hard work, you can control them pretty well.
About two months ago I noticed the first aiptasia in my tank and they started spreading quickly after I thought I'd killed it with kalk paste. I bought six peppermint shrimp (thanks Archit!) and they killed about half the aiptasia in the first few days. There are still a few aiptasia left in the tank but their numbers seem to be diminishing and, to be honest, as long as they aren't spreading, I'm OK with having a few in the tank. I probably feed my tank enough that the peppermint shrimp aren't hungry enough to go after the aiptasia.
Only downside of the peppermint shrimp is that I was considering getting a pair of flame hawkfish but had to bail on that idea when I found out that hawkfish eat the shrimp :-(
peppermint shrimp will deff do the trick. the thing is though you need like 6-8 or more peppermint to do it. they gang up on the aptasia and surround it then start eating them. my dad had a massive outbreak of them and then once we got him bunch peppermints they destroyed them within a month or 2. The file fish we put in did ok but wasn't the best at eating them.