From where to get certificate at client end... Is it is something to ask from the team implementing the server??
You get a certificate from one of two places. First, if its for use within the organization and the organization runs its own PKI, then you get the PKI team to issue you a certificate.
If you need the certificate to be trusted outside the organization by many/most user agents, then you go to the CA Cartel. The cartel includes members like Symantec and VeriSign (in addition to the browsers).
There are members of the cartel who issue certificates for free. They are StartCom, CAcert and possibly Let's Encrypt. While they issue for free, they may charge for revocation because that's where the cost lies.
Don't I need to ask payment gateway support team for certificates or I can get that on my own ??
In this case, see if the Payment Gateway supports client certificates. If they do, get them to issue you one. If they don't then ask them what to do.