Hi @RohitPatil,
Okay, I was able to replicate the issue. It is currently working for basic auth
https://{myinstance}.atlassian.net/rest/api/1.0/users/picker?fieldName=customfield_10087&showAvatar=true&query=
but fails using OAuth 2 as you’ve mentioned.
After further digging, unfortunately, it seems like you are experiencing an existing bug as mentioned in this topic Createmeta field autoCompleteUrl OAuth 2.0 is not enabled for this method.