Find out the project name of assignee
On assignee's name which ticket is open,closed
I am looking for the above solution using REST API
I think there is a deeper question in your mind, but I do not think you have explained it in full.
The easy answer to your question is "Read the issue. When you fetch an issue over the REST API, you can include all its history, from which you can work out who was assigned and when".
But I suspect you're asking more?
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