This is mutual TLS. There are not a lot of standards on how this is done. The server has a list of CAs that it trusts. Your client cert must come from one of those CAs or chain up to one of them. Sometimes the server will advertise the list of client hints, some hide them. If hidden, you have to talk to the server owner.
Running 'openssl s_client -connect server:port' will give you some data. Client hits would look like this
---
Acceptable client certificate CA names
C = US, ST = California, L = San Francisco, O = "company.com, inc.", CN = company.com Root CA 1
C = US, ST = California, L = San Francisco, O = "company.com, inc.", CN = company.com Internal Root CA 4
C = US, ST = California, L = San Francisco, O = "company.com, inc.", CN = company.com Internal Root CA 3
Requested Signature Algorithms: Ed25519:Ed448:ECDSA+SHA256:ECDSA+SHA384:ECDSA+SHA512:RSA-PSS+SHA256:RSA-PSS+SHA384:RSA-PSS+SHA512:RSA-PSS+SHA256:RSA-PSS+SHA384:RSA-PSS+SHA512:RSA+SHA256:RSA+SHA384:RSA+SHA512:ECDSA+SHA1:RSA+SHA1
Shared Requested Signature Algorithms: Ed25519:Ed448:ECDSA+SHA256:ECDSA+SHA384:ECDSA+SHA512:RSA-PSS+SHA256:RSA-PSS+SHA384:RSA-PSS+SHA512:RSA-PSS+SHA256:RSA-PSS+SHA384:RSA-PSS+SHA512:RSA+SHA256:RSA+SHA384:RSA+SHA512
Peer signing digest: SHA256
Peer signature type: RSA-PSS
Server Temp Key: X25519, 253 bits
---