“what are human’s closest living relatives that live in north america, since there are no primates in north america”
As with all specific phylogenetic questions, allow me to preface this answer with
Genetics never has and never will be my strong suit, so I’m always cautious talking about it. Not to mention that it seems like these days anybody with electricity and some agarose is publishing new and conflicting phylogenetic trees. And yes, I am looking directly at you, bat geneticists. But I digress.
Just to clarify, there are primates in North America - all kinds of monkeys cavort about in Mexico and Central America, but I’m assuming you specifically mean the US and Canada. Excluding the smaller sister taxa that also aren’t found in North America*, the closest relatives of primates in the US and Canada are Rodentia and Lagomorpha - meaning rodents and rabbits/hares/pikas.
*treeshrew phylogenetic placement is pretty wonky in and of itself, so I’m not even gonna GO there. Just know that they are in the vicinity of primates