I do have private key(my_ca.key) and public key(my_cert.crt) which is signed by DigiCert. Now I want to generate the SSL certificate (version 3) and sign it by my private ke
Normally all X.509 certificates in certificate chain except the last one are CA certificates. The first certificate in chain is called root CA (in your case DigiCert High Assurance EV Root CA), then other CA certificates in issuer chain (if any) are intermediate CAs and the last one is End Entity (not CA). I don't think you can issue new SSL certificate issued by non-CA certificate. So you can use my_cert.crt signed by DigiCert as SSL certificate but you cannot issue your own using my_ca.key.