Yes you can appear in the Staff Selection Commission, while doing internship in BHMS. The basic requirements for the SSC are as following:

Eligibility:
The applicant should have completed graduation good academic record from any recognized university of India.

Age limit:
Age should be 18-25

After completing Bachelor of Homeopathic medicine and surgery you can apply for following types of the positions:

Government homeopathic medical officers
Homeopathy lecturer and pharmacist-cum-dispenser.
Reader
Homeopathy professor, reader and lecturer