Cassandra doesn't allow for range queries on partition key.
One way of dealing with this problem is changing your schema so that your timestamp value would be a clustering column. For this to work, you need to introduce a sentinel column as partition key. See this question for more detailed answers: Range Queries in Cassandra (CQL 3.0)
Another way is just to let Spark do the filtering. Range queries on primary key should work in Spark SQL. They would simply not be pushed down to Cassandra and Spark would fetch all data and filter them on the Spark side.