Hi Shubham,

Please find the below explanation which might be helpful for you.

There are two solutions that I see here. It sounds to me like you are having an issue with users cases being reassigned to a queue or something every time they edit a case and the assignment rule is triggered. 

1. You can use two assignment rules. The first would look to see if a case with a specific record type is already assigned to a specific user and if so, use "same User". This will prevent the case from being reassigned. Then a second Assignment Rule could be used to catch all other cases of that record type to assign to the user or queue. All page layouts would have "Use Active Assignment Rules" enabled. 

Example: 
Rule 1: (Case: Case Record Type EQUALS Technical Support) AND (Case: Case Owner EQUALS Troy Center, Bob Smith, Robert Davis)
Assign to: same User

Rule 2: Case: Case Record Type EQUALS Technical Support
Assign to: Technical Support Queue (or one of the users)

2. You can use Case Assignment Rules to assign the cases when created, however, all page layouts have "Use Active Assignment Rules" disabled. In this scenario, you would change a case record type AND have to then change the owner manually or using workflow rules. 

You could also use a hybrid of these two methods. There are other people in here talking about using Case Assignment on creation, then use workflow rules to manage case assignment based on other criteria or status, and disable the assignment rules on the page layouts. 

Please mark this as solved if the information helps so that it results in helping others who are encountering a similar issue.

Best Regards,
Nagendra.