According to mysql documentation (https://dev.mysql.com/doc/refman/5.7/en/comparison-operators.html#operator_between) the syntax for BETWEN is
expr BETWEEN min AND max
it is not
expr BETWEEN blabla=min AND stuff=max
Also, it is rather pointless to be using constants in all three expressions, because in this case the result will be known in advance (either always TRUE or always FALSE) without having to consult the values in your table.
It is kind of hard to give you an example without knowing the structure of your table, but what you probably want is something like
WHERE '2017-01-29' BETWEEN start_date
AND end_date
(assuming start_date and end_date are columns in your table)
or something like
WHERE some_column BETWEEN '2017-01-28'
AND '2017-01-31'
(assuming some_column is a column in your table.)