Intra-cluster similarity metric
I would like to know which metrics can be useful to do such things


Since you are clustering your data, why not use the same metric that you used during clustering for comparing your data inside your clusters? I assume this should technically give you exactly what you need. 


  there is no threshold to tell whether individuals in a cluster share similar pattern or not


This hardly depends on your data and what you want to do with your similarity. If you just want to retrieve the most similar point, you can do it pretty straight forward.

If you, on the other hand, want to remove outliers using this measure, you can surely also do so, but you might as well just use an algorithm that deals with outliers in the first place.