Your JSON is incorrect. This should be the correct JSON
String json = "{\"drug\": \"a:1:{s:6:\\\"drug_0\\\";a:3:{s:11:\\\"drug_name_0\\\";s:4:\\\"Napa\\\";s:13:\\\"drug_dosage_0\\\";d:1;s:15:\\\"drug_duration_0\\\";d:1;}}\"}";
JSONObject jsonObject = new JSONObject(json);
String drug = jsonObject.getString("drug");
Using this you can get value of drug
as a:1:{s:6:\"drug_0\";a:3:{s:11:\"drug_name_0\";s:4:\"Napa\";s:13:\"drug_dosage_0\";d:1;s:15:\"drug_duration_0\";d:1;}}