How to make List's Add method protected, while exposing List with get property?

As others have said, you are looking for the .AsReadOnly() extension method.

However, you should store a reference to the collection instead of creating it during each property access:

private readonly List<SomeOtherClass> _items;

public WhatClass()
{
    _items = new List<SomeOtherClass>();

    this.Items = _items.AsReadOnly();
}

public ReadOnlyCollection<SomeOtherClass> Items { get; private set; }

This is to ensure that x.Items == x.Items holds true, which could otherwise be very unexpected for API consumers.

Exposing ReadOnlyCollection<> communicates your intent of a read-only collection to consumers. Changes to _items will be reflected in Items.

You're looking for the ReadOnlyCollection<T> class, which is a read-only wrapper around an IList<T>.

Since the ReadOnlyCollection<T> will reflect changes in the underlying list, you don't need to create a new instance every time.

For example:

public class WhatClass {
    public WhatClass() {
        _SomeOtherClassItems = new List<SomeOtherClass>();
        SomeOtherClassItems = _SomeOtherClassItems.AsReadOnly();
    }

    List<SomeOtherClass> _SomeOtherClassItems;

    public ReadOnlyCollection<SomeOtherClass> SomeOtherClassItems { get; private set; }
}

Use List<T>.AsReadOnly:

public ReadOnlyCollection<SomeOtherClass> SomeOtherClassItems
{
    get
    {
        return _SomeOtherClassItems.AsReadOnly();
    }
}

This will return a ReadOnlyCollection, which will throw an exception if a client calls Add through the interface. In addition, the ReadOnlyCollection type does not expose a public Add method.