Can a public key be used to establish a connection to a server?

Question

Digital certificates

We carry out integration with a third-party developer. The host rejects the connection, and when we asked about possible reasons, we were given a DER certificate with a public key. I have already dug up half of the Internet, everyone writes how to organize such an authorization, but not how to log in.
Actually, for authorization, a private key is usually used, and the public key must be on the server. How can the public key of the server help me so that I can connect to it and the server does not reject the connection?
Key content:

Version: 3 (0x2)
Signature Algorithm: sha256WithRSAEncryption
      Subject Public Key Info:
            Public Key Algorithm: rsaEncryption
                Public-Key: (1024 bit)
                Modulus:
                    00:00:00...
      X509v3 extensions:
            X509v3 Subject Key Identifier:
                00:00:00...
Signature Algorithm: sha256WithRSAEncryption
      00:00:00...

Answer 1

I don’t know what you are integrating with what, but you better read about how this is done in ssh. The principle is quite simple - the server generates a key pair and you generate a key pair. In order for the server to cling to you, you need to register its public key in your config. So that you can cling to him - accordingly, he must register for himself.
To be honest, I don't know how to apply this to your case.

Answer 2

Are you sure that the key is needed for authorization, and not just for establishing an ssl connection?
Who issued their certificate? There is a possibility that they are using a self-signed certificate, which is why they sent you the public key so that you add it as a trusted one manually.