Considering the following code:
class MyClass
{
    ...
};
template <typename Object>
class List
{
public:
    void insert(const Object & x)
    {
        // call when Object is MyClass
    }
    void insert(const Object & x)
    {
        // call when Object is MyClass*
    }
}
int main()
{
    MyClass a;
    List<MyClass> lst;
    List<MyClass*> plst;
    lst.insert(a);
    plst.insert(new Myclass);
    return 0;
}
How to tell the compiler call different methods based on if the template is a class or a pointer?
How to fix the code above?
You can use a combination of std::is_pointer and std::enable_if:
#include <type_traits>
#include <iostream>
class MyClass
{
};
template <typename Object>
class List
{
public:
    template<class T=Object>
    void insert(T t, typename std::enable_if<std::is_pointer<T>::value >::type* = 0) 
    {
        std::cout << "insert pointer" << std::endl;
    }
    template<class T=Object>
    void insert(T t, typename std::enable_if<!std::is_pointer<T>::value >::type* = 0) 
    {
        std::cout << "insert non-pointer" << std::endl;
    }
};
int main()
{
    MyClass a;
    List<MyClass> lst;
    List<MyClass*> plst;
    lst.insert(a);
    plst.insert(new MyClass());
    return 0;
}
Live example: https://ideone.com/CK8Zdo
This will allow you to insert both pointers and non-pointers into a pointer or non-pointer list. If you want to restrict that, you can use this:
#include <type_traits>
#include <iostream>
class MyClass
{
};
template <typename Object>
class List
{
public:
    template<class T=Object>
    void insert(T t, typename std::enable_if<std::is_same<T,Object>::value&&std::is_pointer<T>::value >::type* = 0) 
    {
        std::cout << "insert pointer" << std::endl;
    }
    template<class T=Object>
    void insert(const T& t, typename std::enable_if<std::is_same<T,Object>::value&&!std::is_pointer<T>::value >::type* = 0) 
    {
        std::cout << "insert non-pointer" << std::endl;
    }
};
int main()
{
    MyClass a;
    List<MyClass> lst;
    List<MyClass*> plst;
    lst.insert(a);
    // plst.insert(a); // compiler error
    // lst.insert(new MyClass()); // compiler error
    plst.insert(new MyClass());
    return 0;
}
Live example: https://ideone.com/3DtBfr
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