Cognition of people born by C-section vs born ordinarily? Has there been any research comparing the cognition of people born via C-section to people born vaginally? 

During a vaginal birth, the baby's head is pressured and deforms somewhat in order to make it through. Hypothetically, this could cause some minor brain damage which would be avoided by C-section birth.
I don't know if there has been any research on this, but there is reason to doubt that such research would yield any meaningful results.

You would need to control for a large number of things to address your question. For example, people born by C-section are people who have access to medical care. Those people have money, which is associated with education and opportunities, both of which are associated with IQ.

Additionally, a C-section is medical intervention for when something goes wrong. The things that lead to C-sections (such as improper positioning of the baby before birth, compromising oxygen supply) can lead to brain damage. C-sections generally are associated with many more complications than healthy vaginal births.

Another thing to consider is that vaginal birth would be a poor evolutionary solution for human reproduction if it lead to significantly lower intelligence.

I would be much less surprised if the opposite of your hypothesis turned out to be true.