Hello, hope you are doing well!
The caste certificate number/serial number is usually written on the top right corner of the caste certificate. It is a number consisting of numerical combinations. It is present in every caste certificate.
So, you can find yours from your certificate and use in your application form or wherever you need to.
For a more specific answer please tell me the name of the college form you are filling or applying into, the college name or the university name, the course name.