I have these normalized counts for a gene under different conditions:

Myc 8.703798652 17.15727528 12.74184922 20.88031384 19.31939574 19.51436733 15.22619271 11.25208598 13.03293781 16.08920907 16.8038009 7.560006805 ...........................!!!

and the basemean is 12 and 8 in two conditions, the P value is also significant

Now my question is ... 1) given this low number of counts, should I trust this data? 2) is it right to just remove these genes with low counts? if yes is there any cutoff value for it?

Thank you in Advance!!

I have no idea which counts are in which group.

DESeq2 uses the distribution of dispersion across all genes, plus a model of the information content of the dispersion estimates, to determine if the difference across groups is more than would be seen under the null. It is more than just looking at the normalized counts.

You can remove low count genes ahead of analysis if you chose but it is not necessary. Additionally, see the DESeq2 paper on the use of an LFC threshold. If you want to prioritize genes with larger effect sizes, I highly recommend setting lfcThreshold.

If you didn't lie to the software, then trust the padj. Otherwise, why bother with the software at all?