If by mistake I have shared the details like Common Name, Serial number, etc.. of the certificate of my intranet site/server that is not exposed to the internet will it help attackers exploit the system?
Those is publicly available information. They are contained in the certificate and you "leak" them to all clients.
What exactly are you concerned about?
Your certificate is meant to be public.
Edit for the edited question:
Yes, those things can make the life of an attacker easier.
- the CN can leak the naming scheme for the network
- the CA can leak information on how it can be breached or impersonated
- the validity gives a rough time slot for when it will most likely be rolled over.
Yet, for all these informations to be useful, an external attacker would need to have access to your internal network.
Other security measures should prohibit this - and if the attacker has access, the data is again more or less public.
The biggest "leak" from my point of view is the naming scheme of the intranet. That makes the discovery process easier for an attacker.
Yet, nothing to freak out about - especially since the client will probably dispose of the information more or less instantly.
In general, certificates are meant to be public. The idea of a certificate containing secret information doesn't really make sense.
That being said, the certificate does contain information about the topology of your intranet (domain names of the servers, CN of your internal CA, etc). Maybe this gives attackers an advantage, maybe it doesn't. If your firewalls are blocking external access to the intranet then it's irrelevant.
Bottom line: There's no crypto or network security reason why this is a problem. It does give attackers some information about the server structure of your intranet. Whether or not this is a problem is something you'll have to decide for yourself - we can't make that call for you.
For example, if the CN of the server contains the name of top secret research project then there's intellectual properly leakage here. If, on the other hand, the CN is like
cn=exchange server, dc=myCompany, dc=com then the attacker now knows that you use Outlook for your email. Big deal.