Hi valentinaorju,

Note: For this sample I have refer below articles. For more details refer below article links.

ASP.Net MVC: Client Side Email Validation using Data Annotation attributes and jQuery

ASP.Net MVC: Email Validation using JavaScript and Regular Expression

Please refer below sample.

Model

public class PersonModel
{
    [Required(ErrorMessage = "Email is required.")]
    [RegularExpression(@"^[a-zA-Z0-9.!#$%&'*+/=?^_`{|}~-]+@[a-zA-Z0-9-]+(?:\.[a-zA-Z0-9-]+)*$", 
        ErrorMessage = "Invalid Email Address.")]
    public string Email { get; set; }
}

Controller

public class HomeController : Controller
{
    // GET: Home
    public ActionResult Index()
    {
        return View();
    }

    [HttpPost]
    public ActionResult Index(PersonModel person)
    {
        return View();
    }

    [HttpPost]
    public JsonResult CheckEmail(string email)
    {
        dbUsersEntities entities = new dbUsersEntities();
        bool isValid = entities.Users.ToList().Exists(p => p.Email.Equals(email, StringComparison.CurrentCultureIgnoreCase));
        return Json(isValid);
    }
}

View

@using (Html.BeginForm("Index", "Home", FormMethod.Post))
{
    <span>Email:</span>
    <input id="txtEmail" type="text" name="Email" onkeyup="CheckAvailability()" />
    @Html.ValidationMessageFor(m => m.Email, "", new { @class = "error" })
    <span id="message"></span><br />
    <input id="btnCheck" type="submit" value="Submit" />
}
<script type="text/javascript" src="https://ajax.googleapis.com/ajax/libs/jquery/1.8.3/jquery.min.js"></script>
<script type="text/javascript">
    function CheckAvailability() {
        $(".field-validation-error").hide();
        $("#message").hide();
        var email = $("#txtEmail").val();
        $.ajax({
            type: "POST",
            url: "/Home/CheckEmail",
            data: '{email: "' + email + '" }',
            contentType: "application/json; charset=utf-8",
            dataType: "json",
            success: function (response) {
                $("#message").show();
                var message = $("#message");
                if (!response) {
                    //Email available.
                    message.css("color", "green");
                    message.html("Email is available");
                } else {
                    //Email not available.
                    message.css("color", "red");
                    message.html("Email is NOT available");
                }
            }
        });
    };
</script>

Screenshot