Q:

Is overriding of a function possible in the same class?

it's an objective question type, but Is overriding of a function possible in the same class? in general, and in C# to be exact. If it is possible how and when can it be used?

A:

This is from the C# Language Specification §10.6.4 Override methods 

The method overridden by an override declaration is known as the
  overridden base method. For an override method M declared in a class
  C, the overridden base method is determined by examining each base
  class type of C, starting with the direct base class type of C and
  continuing with each successive direct base class type, until in a
  given base class type at least one accessible method is located which
  has the same signature as M after substitution of type arguments. For
  the purposes of locating the overridden base method, a method is
  considered accessible if it is public, if it is protected, if it is
  protected internal, or if it is internal and declared in the same
  program as C.
A compile-time error occurs unless all of the following are true for
  an override declaration:

An overridden base method can be located as described above.
There is exactly one such overridden base method. This restriction has effect only if the base class type is a constructed type where the
  substitution of type arguments makes the signature of two methods the
  same.
The overridden base method is a virtual, abstract, or override method. In other words, the overridden base method cannot be static or
  non-virtual.
The overridden base method is not a sealed method.
The override method and the overridden base method have the same return type.
The override declaration and the overridden base method have the same declared accessibility. In other words, an override declaration
  cannot change the accessibility of the virtual method. However, if the
  overridden base method is protected internal and it is declared in a
  different assembly than the assembly containing the override method
  then the override method’s declared accessibility must be protected.
The override declaration does not specify type-parameter-constraints-clauses. Instead the constraints are
  inherited from the overridden base method. Note that constraints that
  are type parameters in the overridden method may be replaced by type
  arguments in the inherited constraint. This can lead to constraints
  that are not legal when explicitly specified, such as value types or
  sealed types.

So no it is not possible, the override modifier is used to extend the base class method not for hiding method definitions in the current class.
Maybe it is possible that your interviewer got confused by method selection after a method has been overridden, for example here.

