Database first , How to implement inheritance in EF6

I would suggest that database inheritance/TPT/TPH is not necessary for this situation. What you need is just an IAuditable interface:

public interface IAuditable
{
    string CreatedBy { get; set; }

    DateTimeOffset CreatedTime { get; set; }

    string ModifiedBy { get; set; }

    DateTimeOffset? ModifiedTime { get; set; }
}

Then you have two options:

1. If you are sure all of your entities will be IAuditable, you can simply change the T4 template so that all auto-generated entities will implement IAuditable.

2. If only some of your entities will be IAuditable, you can add partial classes to those auditable entities like:

   public partial class Foo
   {
       // Auto-generated properties by EF
       public int Id { get; set; }
       ...
   } 
   

   Then in another file:

   public partial class Foo : IAuditable
   {
       // No implementation because auditable fields already exists
   }
   

You can then derive an abstract class from DbContext to automatically update these IAuditable properties:

public abstract class AuditableDbContext : DbContext
{
    public override int SaveChanges()
    {
        UpdateAuditableProperties();
        return base.SaveChanges();
    }

    public override async Task<int> SaveChangesAsync()
    {
        UpdateAuditableProperties();
        return await base.SaveChangesAsync();
    }

    public override async Task<int> SaveChangesAsync(CancellationToken cancellationToken)
    {
        UpdateAuditableProperties();
        return await base.SaveChangesAsync(cancellationToken);
    }

    protected virtual void UpdateAuditableProperties()
    {
        var now = DateTimeOffset.Now;
        var userName = GetUserName();
        var changedAuditableEntities = from entry in ChangeTracker.Entries<IAuditable>()
                                       let state = entry.State
                                       where
                                           state.HasFlag(EntityState.Added) ||
                                           state.HasFlag(EntityState.Modified)
                                       select entry;

        foreach (var auditable in changedAuditableEntities)
        {
            var entity = auditable.Entry;

            switch (auditable.State)
            {
                case EntityState.Added:
                    entity.CreatedDate = now;
                    entity.CreatedBy = userName;
                    break;
                case EntityState.Modified:
                    entity.ModifiedDate = now;
                    entity.ModifiedBy = userName;
                    break;
            }
        }
    }

    protected abstract string GetUserName();
}

Your DbContext can derive from AuditableDbContext and then implement GetUserName() to supply the username who creates/modifies the entities.