why don't you try HttpResponseMessage at api side? you will be easily able to return response with custom message.
Your method will be something like:
public async Task<httpresponsemessage> Put(List<string> emp, int ID)
{
Employee tt = tst.Employee.Find(ID);
if(tt == null)
{
return Request.CreateResponse(HttpStatusCode.BadRequest, "No Record Found");
}
int id = Convert.ToInt32(emp[3]);
int id1 = Convert.ToInt32(emp[2]);
tt.Id = id;
tt.Name = emp[1];
tt.Salary = emp[0];
tt.Age = id1;
tst.SaveChanges();
return Request.CreateResponse(HttpStatusCode.OK, "success!");
}
</string></httpresponsemessage>
* Mark as solution if it's helpful for you.