If you aren't overrun and it seems to be working, I'd stick with the soap every 2-3 days until you haven't seen any for a while. Drench them really well, wait a few minutes and rinse.

Yep, I would give the insecticidal soap a chance to work. If that doesn't work, you can go with a chemical insecticide or even a batch of lady bugs.
Bruce

I have 32 pepper plants of various kinds and I found some aphids today.

I just position myself so that the sunlight shines through the leaves and I can see the aphid shadows through them.

Then I smoosh the aphids with my fingers; easier than soap and I don't have to get my leaves wet.

Luckily the aphids have been staying off my peppers, and I think I found out why the other day. Was walking by some hickory saplings and noticed there was something odd under the leaves. Stopped for a closer look and there was just a solid sheet of aphids under there. They almost looked like fungus or mold they were so thick.

So, note to self, hickory trees = aphid bait.

So far, they haven't come back so maybe the soapy water helped. Not sure if I have the stomach to squish them bare-handed.. lol.

It's kind of gross, yep; but I've become less squeamish about things like that since last year. I won't squish larger bugs, but aphid and smaller is alright (for me).

If you see ants crawling up your peppers, and they aren't headed to the flowers, check again. The ants like to 'herd' them there so they can 'farm' them; which creeps me out.

A flashlight beneath the leaves so you can see the shadows through them helps.

I've had a battle with aphids this year. I think I'm finally on the upswing. I bought some ladybugs to bolster the ones already in my garden. I know they go everywhere but a lot are sticking around and my pests sure seem to be dwindling. Last night I saw 5 ladybugs working one pepper plant. And others had a few on them too. It was a week ago that I released the extras. I think they are doing good. I had to use 2 rounds of sevin while the seedlings were in trays going in and outside waiting on the weather. I don't like to use poison but they were rampant and taking over. Since they weren't in the garden and not available to the ladies I had little choice. I won't spray them now (nor do I need to) and risk wiping out the ladies and any other good bugs. Most years aphids aren't an issue. I never would have thought ladybugs would be my saviors. As it gets hotter out I'll keep an eye out for a re infestation and I have read in the higher temps lacewings are better. I'm sure impressed so far.