Strange odds ratio (OR) derived from Fisher's test

I have frequency data for about 1000 genetic marker for two groups that I want to compare them between the two groups. I used Fisher’s test (in R) on the count data and got FDR and odds ratio (OR) for each marker; But, the OR range is strange (0.003-500). Could you please kindly let me know how I can interpret OR in this case or validate it by another test?

• I am not sure whether I understand the structure of your data. Ertxiem assumes in the nswer that your sample size might be small which makes sense in case of latge confidence intervals. But what do you mean with "1000 biomarkers"? 1000 wouldn't be a small sample size at all... – user247233 May 14 '19 at 9:05

Since the confidence interval you presented includes the value $$1$$, it means that we should not reject the null hypothesis: $$OR = 1$$. This means that the odds of a positive event appearing in one group is not significantly different from the odds of a positive event appearing in the other group.
I've assumed in my answer that what you called "OR range" with the values $$[0.003; 500]$$ to the $$95\%$$ confidence interval for the OR.