The best of this so called evidence I have seen is some guy from the University of Virginia (I just looked it up and it looks like there is now a department that works on it:
https://med.virginia.edu/perceptual...es-of-previous-lives/fifty-years-of-research/) who compiled a list of children who claimed they were reincarnated and tried to match their accounts with dead people.
I can't remember exactly what but I know there have been multiple criticisms of the work being done, especially regarding potential coercion of the children (for example the parent encouraging the child to believe in reincarnation or the child just making things up based on things they have already seen/ been exposed to. There are some news articles on it.
That being said, I've always been extremely skeptical of the existence of god and the concept of heaven since I can first remember, but apparently my father asked me when I was very young (like at 3 - old enough to have just started forming complete and moderately complex sentences but young enough to not remember anything) whether or not I remembered heaven. Apparently I told him I did in fact remember heaven well, which was probably younger me making things up, but it still freaks me out (I feel somewhat confident my younger self would not have said that under normal circumstances... but also I was 3). When I was 5 and he asked again I apparently told him I did not remember heaven at all. So who am I to say for sure?