要实现ASP.NET Core 3和EF Core 3的远程验证，可以按照以下步骤进行操作：

1. 创建一个ASP.NET Core 3的Web应用程序项目。

2. 安装必要的NuGet软件包：Microsoft.AspNetCore.Mvc.Razor.RuntimeCompilation、Microsoft.EntityFrameworkCore、Microsoft.EntityFrameworkCore.SqlServer和Microsoft.EntityFrameworkCore.Tools。

3. 在Startup.cs文件中配置服务和中间件：

public void ConfigureServices(IServiceCollection services)
{
    services.AddControllersWithViews();
    services.AddRazorPages().AddRazorRuntimeCompilation();
    
    // 添加数据库上下文
    services.AddDbContext(options =>
        options.UseSqlServer(Configuration.GetConnectionString("DefaultConnection")));

    // 添加远程验证服务
    services.AddScoped();
}

public void Configure(IApplicationBuilder app, IWebHostEnvironment env)
{
    // 省略其他配置
    
    app.UseStaticFiles();

    app.UseRouting();

    app.UseEndpoints(endpoints =>
    {
        endpoints.MapControllerRoute(
            name: "default",
            pattern: "{controller=Home}/{action=Index}/{id?}");
        endpoints.MapRazorPages();
    });
}

4. 创建一个名为ApplicationDbContext的数据库上下文类：

public class ApplicationDbContext : DbContext
{
    public ApplicationDbContext(DbContextOptions options) : base(options)
    {
    }

    public DbSet Users { get; set; }
}

5. 创建一个名为User的模型类：

public class User
{
    public int Id { get; set; }
    public string Name { get; set; }
    public string Email { get; set; }
}

6. 创建一个名为IRemoteValidationService的接口，用于定义远程验证的方法：

public interface IRemoteValidationService
{
    Task IsEmailUnique(string email);
}

7. 创建一个名为RemoteValidationService的服务类，实现IRemoteValidationService接口：

public class RemoteValidationService : IRemoteValidationService
{
    private readonly ApplicationDbContext _dbContext;

    public RemoteValidationService(ApplicationDbContext dbContext)
    {
        _dbContext = dbContext;
    }

    public async Task IsEmailUnique(string email)
    {
        return await _dbContext.Users.AnyAsync(u => u.Email == email) == false;
    }
}

8. 在User模型类中添加远程验证的特性：

public class User
{
    public int Id { get; set; }
    public string Name { get; set; }
    
    [Remote(action: "IsEmailUnique", controller: "Validation", ErrorMessage = "Email already exists.")]
    public string Email { get; set; }
}

9. 创建一个名为ValidationController的控制器类，用于处理远程验证的请求：

public class ValidationController : Controller
{
    private readonly IRemoteValidationService _validationService;

    public ValidationController(IRemoteValidationService validationService)
    {
        _validationService = validationService;
    }

    [AcceptVerbs("GET", "POST")]
    public async Task IsEmailUnique(string email)
    {
        var isUnique = await _validationService.IsEmailUnique(email);
        return Json(isUnique);
    }
}

完成以上步骤后，当用户输入Email时，远程验证将会在服务器端执行，检查是否存在相同的Email。如果存在，则返回错误消息。