How to compare more than two matched medians My sample consists of 30 patients.
These patients had three times of hormonal dose measurement:
Time 1, Time 2, Time 3. So 3 three measurements.
The aim is to evaluate whether the average dose (in the blood) of hormone varies over time.
The distribution of the hormone dose is not normal. So I decided to do a non-parametric test.
Is the Kruskal-Wallis test the most appropriate? Can the Kruskal-Wallis test be applied to paired data?
I did some research on the Kruskal-Wallis test, but I found little literature on the analysis of paired data.

It sounds like you have an experiment arranged in unreplicated complete block design.  If so, traditional nonparametric tests are Friedman test and, maybe preferably, Quade test.  Here, Patient is the block and Time is the factor of interest.  You could also use aligned ranks transformation anova as a nonparametric test.
Any of these approaches have appropriate post-hoc procedures to determine which Time differs from which other Time.
As an aside, none of these approaches, nor the Kruskal-Wallis test, is generally a test of the medians.  If you were really interested in medians, you could use mixed-effects quantile regression.
