I have some data I am working with, and I am curious if I am able to combine p-values from a paired t-test for CpG sites in the genome using Fisher's Method to get one p-value for each unique gene. Linked here is the Wikipedia page for Fisher's Method. I understand that an assumption of the method used is that each individual p-value being combined must be independent. I'm relatively new to biostatistics, so I'm curious if using CpGs from the same gene would violate this assumption.
Methylation levels have high local correlation, so Fisher's method would be problematic. Having said that, you have no reason to use Fisher's method after a paired t-test. A paired t-test will give you a single p-value per gene, which is what you want. Do be sure to only include CpG with some minimal coverage in both group.
What is typically done in methylation analysis is to assess the islands of methylations.
Check this workflow, in the section linked it uses some predefined islands for instance. I am no expert on this area but you could asses if the islands or certain regions are more methylated than expected.