Doing the database operations, inside the JSP.. A Strict
NO.
Java code inside JSP, was discredited 10 Years back. Move the Logic to
Servlets.
As far as your problem is concerned. The solution may be like this.
In your registration.jsp, a small hyperlink, can be made next to username, as checkAvailabality. Once User clicks this, a AJAX operation will be made, that AJAX returns a status as username available or not available, so based on this, a appropriate div in a JSP will be updated. The backend also, as to do validation, before inserting into database and return back the error message, this is for the case if user doesn't use the checkAvailablity link, and just clicks Submit.
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