We have a table with column period defined as timestamp datatype to store date and time, when day l

We have a table  with column period defined as timestamp datatype to store date and time, when day light saving  sets back one hour, we have duplicated the times , and the period is a unique key.  how to avoid this issue?
Would changing timestamp datatype to timestamp with time zone address this issue?

Also how should java  insert to the table?
The java code we have right now is the following

quickviewInsertStatement.setTimestamp(1, new Timestamp(start.getTime()));