What happened to Adam in the earlier cycles once he killed these characters?

In all the earlier cycles, what did Adam do once he realized killing Martha's child isn't the answer as he was still alive after doing so.

Killing Martha's child hasn't been a constant. It is also a fairly recent addition to the circle, just as Claudia's appearance is.

Important to note, we don't specifically know how often each new addition fails before it succeeds. No one seems to have perfect knowledge of the cycles and what happened in earlier cycles.

Claudia has some notion due to her bootstrapped notebook, but even she states to Adam that she thinks that her conversation with Adam is happening for the first time, she doesn't know it for sure.

It's possible that this Claudia/Adam conversation happened before but did not lead to breaking the cycle, Adam didn't believe her, or Adam didn't succeed in bringing Jonas where he needs to be.
Failing to break the cycle then causes another cycle and another attempt for Claudia to convince Adam and Adam to put Jonas on the right path.

All we know for sure is that we see the last cycle in the finale (and even that is open to fan theories...)

So the short answer is that we don't know. But there is another part to consider: what is Adam's plan? He clearly has everything planned, so what does he intend to do?

First of all, remember that there are two alternate timelines.

One thing that's important to mention is that Adam only has access to one time travel device: his 1920 machine. He doesn't have the suitcase or the golden ball. And the 1920 machine doesn't travel with you, so it's a one way trip.

If you look at the Schrödinger-A dimension where he shoots Martha and alt-Martha saves Jonas, him killiing Martha happens so close to the apocalypse that there is no way for him to get away from the blast. He walks outside, and has no way of travelling away from 2019.
The reasonable assumption therefore is that he dies, knowingly. It makes sense when you consider that his life's work is to complete the circle, and doing so is his last mission. He achieves it by killing Martha

When in the Schrödinger-B universe, the one where Bartosz distracts alt-Martha and she doesn't save Jonas, who instead took shelter in the basement, Adam ends up in 2053 where he kills pregnant alt-Martha.

Here, Adam does have access to another travel device, alt-Martha's golden ball (also the power plant itself, but that is not confirmed to allow for cross-world travel, and Adam would be traveling from his world to Eve's).

In the finale, when he visits Eva, Eva expects him to kill her, "as it always happens". This suggests that Adam, having killed alt-Martha, then travels to Eva and kills her too. It's unclear what happens after that.
You would suspect that the Unknown doesn't let Adam get away with it, but we don't know for a fact if the Unknown is in Eva's headquarters at the time.

However, even though he did still kill alt-Martha, the "last" Adam still travels to Eva, but now doesn't kill her, instead making amends and enjoying the cycle finally being broken.

I think this isn't explained in all the details, but one thing that happens is that he kills Eva. After the last cycle in season 3, he goes to Eva but this time with an empty gun. Eva mentions she is prepared to be killed, as he always used to do it.