I applied a logistic regression with a covariate for nationality of the individual. In total there are more than 60.000 SNPs which show a significant influence of the covariate. In particular, the most crucial SNP rs2222162 shows a p-value < 10^-4 and the additive coefficient is 10^-5

My question is : How to continue ? Now I know that there is a population structure, how do I draw further conclusions using my logistic regression model ?

Try to use JMP software and Next Gene software, perhaps R packages can be helpfull too. Regarding Logistic regression --- you can find several monographs by Springer. Logistic regression has 0 or 1 outcome and several input predictors-parameters-arguments to weight their importance and influence. Less P value is better --- I think you know that...