Hello. Could you give a few more details?

• What does your matrix look like - how many OTUs / species are there in the matrix? How complete is it? How distantly related are your OTUs?
• How did you choose your models for each gene? Are you inferring phylogeny or a clock? If the clock, have you enforced a topology?
• Did the ESS for gamma.shape.3 max out early and never increase further, or is it still increasing after 100 million iterations? (which sounds like a lot).

In any case, it doesn't sound like you are using a great deal of data; 4 genes might not be enough to provide phylogenetic signal, which is manifested in your gamma shape not converging. These days, it is also quite unusual to use mitochondrial sequences for phylogenetics, and in particular clock inference, as mtDNA seems to be highly variable in rate, and be subject to unusual evolutionary effects, especially as they go through selective sweeps once per generation in the maternal germline.

mtDNA hypervariability

https://academic.oup.com/mbe/article/25/1/120/1097840

Article The erratic mitochondrial clock: Variations of mutation rate...

Article Watching the clock: Studying variation in rates of molecular...

Hello Alastair,

thank you for your answer. The matrix consists of 36 species (51 specimens, 6 genera which are close relatives). One gene is complete and other genes lack 4 or 6 sequences (the genes have been treated by g-block and for saturation). The models of genes were selected by JModeltest. I'm not sure about moving the ESS value depending on MCMC chain length ( I set a straight higher number).

The first issue is why are you trying to estimate that parameter? Who cares? More constructively, I suggest you examine the trace, sometimes increasing burnin will sort things. Sometimes the chains have not converged.