Create a new script in /etc/init.d/myscript.
vi /etc/init.d/myscript
(Obviously it doesn’t have to be called “myscript”.) In this script, do whatever you want to do. Perhaps just run the script you mentioned.
#!/bin/sh
/path/to/my/script.sh
Make it executable.
chmod 755 /etc/init.d/myscript
Configure the init system to run this script at startup.
update-rc.d myscript defaults
ystem to run this script at startup.
update-rc.d myscript defaults