As I read your question, you could mean two things.
First ,if if you want a function in Class A that can be overriden in Child Class B but is not visible to any outside class:
public class ClassA
{
protected virtual ReturnType FunctionName(...) { ... }
}
public class ClassB
{
protected override ReturnType FunctionName(...) { ... }
}
Second, if you want to force an implementing class to define the function:
public abstract class ClassA
{
protected abstract ReturnType FunctionName(...);
}
public class ClassB
{
protected override ReturnType FunctionName(...) { ... }
}
Another concept you might look at if you are just digging into C# that is kinda related is partial classes. This is the idea of two source files being combined at compile time to create one class, both from the same assembly:
File 1:
public partial class ClassA
{
private ReturnType FunctionName(...);
}
File 2:
public partial class ClassA
{
//actual implimentation
private ReturnType FunctionName(...){ ... };
}
Partials are not widely used except when dealing with designed-generated files, like the Linq2Sql files, or EDM, or WinForms, etc.