How to handle non normally distributed residuals

Currently we are working with a GEE model, at this point we are having doubts about our residuals which are not normally distributed. Log transformation is not an option, as we have also negative data points.
I have been reading some post and articles, but it is not clear to me what non -normally distributed residuals exactly mean for our p-value.

Is there some one who can explain me this or refer me to some article(s)/book?