Since MEDIPS can support edgeR as a diff.method, is it possible to add a covariate to the differential analysis (e.g. cell-type) or alternatively use a paired t-test for the "ttest" diff.method?

Thanks

MEDIPS supports the use of edgeR exactTest, which does not accept covariates. Neither do t-tests, so if you want to use a model that includes other covariates you will likely need to use a different package.