Hello Dipika Das,
Thank you for your post in this Q&A forum.
The only way to determine if the email has any conversation thread is by using filter, you can do GET, messages?$filter= conversationId eq 'conversationId of the email is in question', this will give you list of conversation messages if there are any, if not it will show only one message.
Here is one example email with some conversations;-
Let me know if that helps.
Thanks
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