I am aware of that multiple testing correction is needed when multiple hypothesis tests are simultaneously performed. However, I am a little confused by the word "simultaneously".

Say I have called somatic variants from hundreds of samples. With this sample-variant matrix, I would like to perform pairwise fisher exact test for variant co-occurrence. Do I need to carry out multiple testing correction on the P-value of each paired variants?

I guess multiple testing correction is needed. However, I can consider that each of the pairwise fisher exact test was carried out individually and each raw p-value represents the significance of correponding paired variants, right?

The reason to use multiple testing correction is that with raw p-values, you accept that 5% is false positive (when using p < 0.05 cutoff, the chance that 5 out of 100 is wrong). Therefore if you have thousands of tests (your pairwise independent Fisher exact test), that means your number of false positives are not acceptable anymore (5% of thousands is too much). Read more about it e.g. here.

The thing is that I am conducting pairwise fisher exact test individually. Everytime I only select one pair of variants and perform the hypothesis test.

How many times do you conduct this test? In other words, how many p-values do you get in total?

I got multiple p-value from multiple hypothesis tests (probably > 100 times). Note though that each test is conducted on different pair of variants. Can I treat them as totally seperate test so that I don't have to apply multiple testing correct?

No you should use multiple testing correction. Multiple testing correction is exactly meant for cases like yours.

You should edit your question to add these information. And maybe a small example. But rule of thumb is always to correct for multitesting if your perform the same tests multiple times (e.g. perform a differential expression test for

eachgene ; each gene will "have" a p-value ; then you should correct for multi-testing)Here is I am confused about:

for a specific gene showing bare raw significant p-value (would not be significant if correction applied), if I happen to calculate the significance for this gene alone, it still be significant because I don't need to perform correction in this case, right?