Custom Picker autocompletedata

Hi, I am learning custom picker field(Custom Picker). Is it possible to display an option list when advanced jql search? I found that when outputting to jql, it uses a call to rest/api/2/jql/autocompletedata, but when looking for a custom picker, there is no call. but i can search through value. In my example value=uuid which is not user friendly. Is it possible to somehow display options when searching, as when creating / editing a task?