It's so wired parse query in array of pointer can't work on 4.4 below and everything working fine for 5 + ,
ParseQuery<ParseObject> firstQuery = new ParseQuery<ParseObject>(CLASSNAME);
firstQuery.whereEqualTo(COLOUMNNAME1, ParseUser.getCurrentUser());
ParseQuery<ParseObject> secondQuery = new ParseQuery<ParseObject>(CLASSNAME);
secondQuery.whereEqualTo(COLOUMNNAME2, ParseUser.getCurrentUser());
List<ParseQuery<ParseObject>> queries = new ArrayList<ParseQuery<ParseObject>>();
queries.add(firstQuery);
queries.add(secondQuery);
ParseQuery<ParseObject> mainQuery = ParseQuery.or(queries);
Second query is array of parse user pointers.
Note : In Android 5 return all matched data in both. in Android 4.4 return all matched data in first query only.