Please suggest me the best suitable test to check false discovery rate of p values after t test. Only two groups were studied for one single observation to collect the data.
According to your description, only t-test should be fine. I would suggest to use simple tool like excel sheet where you can find option to select your parameter (see attached). If you are applying some drugs, e.g., groups before and after treatment then go for paired otherwise unpaired with unequal variance. If you do not know whether your mean value is increasing only as expected then go for one tail otherwise two tail. If you have only two groups, you do not need post-hoc corrections. If you have more questions regarding this you may mail me.