How would we test for significant changes in expression when many of the normalised counts are clustered together? I've been handed RNA-seq data with a lot of associated covariates.
This data has been put through the DESeq2 package and as a result normalised the data.
One of the transcripts of interest still has non-normal distribution for two genotypes. This is because many of the normalised counts are now clustered around a value of 4.

This is making it tricky to perform statistical tests because in order to perform parametric tests (in this case I want to perform a ANCOVA or multiple linear regression to include the covariates) the data must be normally distributed.
I also don't want to use a non-parametric test because I can't include all the covariates.
Should I just perform parametric tests ignoring this violation or do I have to just perform non-parametric on all my data for a fair comparrison?
Or is there another alternative option I am missing?
Thanks in advance
TLDR- just do the analysis in DESeq2 (it can handle multiple covariates)
If I've interpreted your question correctly there seem to be a few confusions here.
First off, for a multiple linear regression aka ANCOVA, one of the assumptions are the residuals are normally distributed - however this is almost never an issue in practice. The distribution of the data is not so important, you make the assumption that the data has come from a population which is continuous and normally distributed that's why you've chosen to do an ANCOVA. But, RNAseq produces count data - not continuous and bounded at zero. You need to be looking at using a Poisson GLM, or negative binomial GLM as done by DESeq2 (lookup overdispersion)
The normalisation done by DESeq is to account for different library sizes,it doesn't transform the data to make it conform to a normal distribution. You'd need to do some form of data transformation to do that, but don't it's unnecessary.
I'd suggest reading the DESeq vignettes and following their standard pipeline.
Hope that is of some help.