Parse and format date
Parsing twice

Instead of parsing dateStr twice, consider passing the Date object you have already constructed to the local time zone into prefix(String).

Calendar vs Date

A Calendar object has arguably better semantics than a Date, so it may be easier to access the individual chronological fields (actually, in your case, just the day component).

Lengthy try-catch block

Your try-catch block in convertUTC(String) spans the entirety of the method, but it's generally recommended to keep them short and to-the-point so that you effectively get a fail-fast mechanism. It's also easier to understand what's the exact code that might plausibly throw the checked Exception, so that it can be easier to refactor in the future.