My dataset is something like:

t1: 40 samples (8 also participate in t2, 6 in t3) t2: 10 samples t3: 7 samples

This implies many participants (samples) are missing in different timepoints.

In general, when you have repeated measures for some but not all of your subjects, you would use a linear mixed model. To do that using edgeR/limma you would use the voomLmFit function, blocking on subject (e.g., you would provide a factor of the subjects to the block argument).