My guess is that you are writing a story about time travel. But to make time travel stories work, you have to do a better job with your pronouns. In sci-fi stories with mulitple timelines, the writer needs to be clear about what happens in the different timeline.

You use the term "exist." In scifi time travel stories there are things than exist in one timeline but not in other timeline. Even in complex time travel stories everything in the story exists in one of the time lines.

You used the phrase "it was discovered that the killer [...] does not exist.

The only way that this sentence could make sense is if the killer existed in one timeline but not the primary timeline. If the killer did not exist in any timeline, then a murder could not have taken place.

The phrase that destroys your story is the phrase: "a detective discovered the body of another man who was murdered "

Your story only mentions one murder.

I really can't figure out what you mean by "another man who was murdered"

In sci-fi time travel stories, it is possible for a person to kill the other version of himself. Your use of the term "another man" implies that the victim was neither the victim or a copy of the victim from a different time line.

What is really infuriating about your story is that you randomly use pronouns but the pronouns could refer to different things.

I assume that the term "this act" in the second sentence refers the protagonist impregnating his grandmother.

Interestingly, shortly after the murder, the girlfriend to the murdered man got pregnant.

It is a time travel murder mystery. Is the pregnant women part of the opening sentence. Assuming that it is, I would have to say:

The pregnancy happened shortly after the murder. The body was discovered two generations before the pregnancy. You state clearly that the protagonist is not the victim, nor could he possibly be the murderer.

The best time travel story that I can come up with is that the boyfriend (who is not the protagonist) was murdered. The protagonist gets the girlfriend pregnant. The then sends the girlfriend and dead body back in time.

But in this folding the timelines there is no way to deduce the relation between the killer and the murder victim.