The script content could be anything, in this example the Raspberry Pi will be rebooted.
Create a folder to store the scripts in /opt/scripts and create a file called remote-reboot.sh:
sudo mkdir /opt/scripts
sudo vi /opt/scripts/remote-reboot.sh
#!/bin/bash
sudo /sbin/shutdown --reboot now
Change ownership and make executable:
sudo chown pi.pi /opt/scripts/remote-reboot.sh
sudo chmod u+x /opt/scripts/remote-reboot.sh
sudo chmod +x /opt/scripts/remote-reboot.sh
Add the user nobody to the list of users who can reboot without a password:
sudo visudo
# ADDED
nobody ALL =NOPASSWD: /sbin/shutdown*
Test script, running this should restart the Raspberry Pi:
/opt/scripts/remote-reboot.sh