How to use dependency injection with inheritance in C#

After some years of experience, I found the Decorator Pattern a perfect fit for this.

Implementation:

// Abstract type
public interface IRepository<T>
{
    Add(T obj);
}

// Concete type
public class UserRepository : IRepository<User>
{
    public UserRepository(/* Specific dependencies */) {}

    Add(User obj) { /* [...] */ }
}

// Decorator
public class LoggingRepository<T> : IRepository<T>
{
    private readonly IRepository<T> _inner;

    public LoggingRepository<T>(IRepository<T> inner) => _inner = inner;

    Add(T obj) 
    {
        Console.Log($"Adding {obj}...");
        _inner.Add(obj);
        Console.Log($"{obj} addded.");
    }
}

Usage:

// Done using the DI.
IRepositoty<User> repository = 
    // Add as many decorators as you want.
    new LoggingRepository<User>(
        new UserRepository(/* [...] */));

// And here is your add method wrapped with some logging :)
repository.Add(new User());

This pattern is awesome, because you can encapsulate behaviors in separate classes without breaking changes and using them only when you really need them.

As asked by you, here is one very basic and crude sample of solving this problem through Composition rather than inheritance.

public class RepositoryService : IRepositoryService
{

    public RepositoryService (IServiceA serviceA, IServiceB serviceB) 
    {
        /* ... */
    }

    public void SomeMethod()
    {
    }     
}

public abstract class Repository
{
    protected IRepositoryService repositoryService;

    public (IRepositoryService repositoryService)   
    {
      this.repositoryService= repositoryService;
    }

    public virtual void SomeMethod()
    {
          this.repositoryService.SomeMethod()

          .
          .
    }
}

public class ChildRepository1 : Repository
{

    public (IRepositoryService repositoryService)  : base (repositoryService)
    {
    }

    public override void SomeMethod()
    {
          .
          .
    }
}

public class ChildRepository2 : Repository
{

    public (IRepositoryService repositoryService, ISomeOtherService someotherService)   : base (repositoryService)
    {
          .
          .
    }

    public override void SomeMethod()
    {
          .
          .
    }
}

Now, the abstract base class and each child repository class here will only depend on IRepositoryService or any other required dependency (refer ISomeOtherService in ChildRepository2).

This way your child repository only supplies IRepositoryService dependency to your base class and you do not need to supply the dependencies of IRepositoryService anywhere.