How to cite in an appendix (and where to put the Citation list) of a PhD thesis?

For a PhD thesis (as indicated in the tags of your question), check your university's reference style guide. I suspect, however, that it doesn't go into that much detail. So: do what you like best, as long as it's clear and coherent.

If you have many citations in the appendix, and you suspect that people will want to read the appendix and main document separately, just maintain two separate lists of citations. It makes each of them shorter, and thus easier to read.

If you have very few citations in the appendix, you can also consider citing them in a different style, such as footnotes. It keeps them separated from the main references, for clarity, but doesn't necessitate to have a full “appendix list of references” if it's very short.