If I have been told that I am the father of my ex-girlfriend’s son but she has another man on the birth certificate, what will happen?

Nothing will happen and you will have no rights in the child unless and until you file a paternity case and get your rights determined. Get an attorney for that.

What do you want to have happen? It's a complicated question. You don't indicate if the ex and the new guy are married, whether you have any contact or involvement with the child, whether you pay child support, etc. If you want rights with respect to the child, you have to take some action, like filing a paternity petition to have DNA testing performed, establish your parental rights if you are the father, establish timesharing, child support, etc. Consult with an attorney to discuss the specifics of your situation and your options.