It shouldn't be me answering the question, but experts in the field of genetics. I can only point to the research that I am aware of. Anyone can use our TROM Curated Search engine that can sort searches by Scientific Papers. Some papers I found seem to be a bit contradictory, yet they are not. This 2018 paper seems more geared towards "there is a biology of intelligence", this 2013 say it is not, and this big 2019 study says "meh" - full here. Finally this paper looks at the controversies surrounding the topic - full here (I did not read this one).
However they all talk about correlation, else they will prove causation by tweaking some genes to obtain results or see causation in people with mental disabilities - first is almost impossible right now, and second is not really proven with certainty. As far as I am aware it is only correlation at best. Regardless, I see several issues with this approach:
1. No one can define intelligence. Maybe Hitler was good at chess and spacial orientation since he managed to invade so many tribes. But he was a very destructive human being killing millions. On the other hand even people with the Down Syndrome, which is seen as mentally impairing, can achieve a lot in terms of "intelligence" - and that's done through their environment (how they are raised). But trying to define intelligence is tricky if not impossible. So then, what are they looking for more exactly?
2. Correlation does not equal causation. People who wear dresses are (statistically) a lot more likely to develop breast cancer. But that's not because of dresses, but because in our culture women wear dresses,
and women are more predisposed to breast cancer. Even in medicine they can't tell you if you will develop cancer or not based on biology (genetics), because it depends if you smoke, exercise, what you eat, etc.. They can, at best, work with statistics and even those are a bad predictor in many cases. Imagine predicting intelligence when you can't even define intelligence properly.
3. Poor predictor for anything relevant. Speaking of predictions, the best predictor for someone's ability to solve problems and so forth (what we may call as intelligence) is still the environment. Take a
human with the best "intelligence genes" who grows up in a normal environment in a poor country, and one without those genes who is trained to be a scientists. See who is "smarter". Sure, maybe (maybe) if
you put both in the same environment the one with the "intelligence genes" may perform better, but we don't know that and to what degree. So, again, environment is still the best predictor of "intelligence".
4. Useless information. Say we discover these "intelligence genes" and there is no doubt about their influence and they do make a big difference between individuals. Now what? Genetically engineer humans? You can't even do that for simple diseases since it is too complex and you cannot know the results after you do it. And, in the end, it will still be about the environment of those humans.
All in all, what we know for sure is that the environment is so powerful in creating behaviors that it can tweak any human into any kind of behavior. See "feral children" for an extreme example. Also, we made a book https://www.tromsite.com/books/#dflip-df_6560/1 and a video https://www.tromsite.com/videos/books/ (Behaving: From Genes to Gender) about the subject.