Here are a few possible solutions to this issue:
Update reminder message
Add verbiage such as "please arrive early to complete your forms".
Change how you view the schedule
Internally the staff members and doctors may need to change their perspective on the schedule. That means that if a new patient is scheduled at 4:00PM, then understand that the patient is going to arrive at 4:00PM. The first 30 minutes will be spent on paperwork and the intake process and the doctor will not see the patient until 4:30PM. This method does not require any changes to appointment reminders or requesting that the patient arrive early.
Schedule multiple appointments
Schedule two appointments for the same new patient with 2 different appointment purposes such as “NP Intake” at 4:00PM and “New Patient” at 4:30PM. Set up appointment reminders (new patient appointment confirmation messages) for only “NP Intake” so that the reminder shows the time you want the patient to arrive rather than the “doctor’s” time. One appointment could be removed/deleted when the patient arrives to keep your stats accurate.
Keep in mind that patients scheduled an appointment time that fits into their busy schedule and are planning to arrive at the agreed upon appointment time, not 15 or 30 minutes early!