You can create a method readSMS() as shown below where you can pass date and time to read the sms from that particular date.

private void readSMS(String date, String time) {
        // Now create a SimpleDateFormat object.
        SimpleDateFormat formatter = new SimpleDateFormat("dd-MM-yyyy'T'hh:mm:ss");
        String selectedDate = date+"T"+time; 
        //For example: selectedDate="09-10-2015"+"T"+"00:00:00";
        // Now create a start time for this date in order to setup the filter.
        Date dateStart = null;
        try {
            dateStart = formatter.parse(selectedDate);
        } catch (ParseException e) {
            e.printStackTrace();
        }

   // Now create the filter and query the messages.
    String filter = "date>=" + dateStart.getTime();
    final Uri SMS_INBOX = Uri.parse("content://sms/inbox");
    Cursor cursor = getContentResolver().query(SMS_INBOX, null, filter, null, null);

    while (cursor.moveToNext()) {
      //perform the operation you want to
    }
    cursor.close();
 }