Web API - Output value

The Linq extension method Where(...) returns an IEnumerable<T>. Where is a filter on a list, and as such will return a list (IEnumerable). You're then calling ToList() to convert it into a List<T>. When you serialize to JSON, IEnumerable<T>, List<T>, and T[] are all represented (correctly) as a JSON array: [{...}, {...}, {...}]

[Authorize]
// ..api/EmpDetails/Id
public IEnumerable<EmpDetail> Get(string Id)
{
    using (WebAPIEntities WE = new WebAPIEntities())
    {
        var emp = WE.TrxDetails.Where(E => E.EmpId == Id).ToList();
        return emp;
    }
}

If you only want a single item, there are a few ways you can do this with Linq:

Single(...) - This will return a value so long as that value is unique in the list. It will throw an error if it isn't found.

SingleOrDefault(...) - This will return a value, or null if it isn't found.

First(...) - This will return the first matching value, or throw an error if there aren't any.

FirstOrDefault(...) - This will return the first matching value, or null if there aren't any.

Last(...) - This will return the last matching value, or throw an error if there aren't any.

LastOrDefault(...) - This will return the last matching value, or null if there aren't any.

The exception type returned by the above is: InvalidOperationException

I'm assuming FirstOrDefault(...) will suffice for your scenario:

[Authorize]
// ..api/EmpDetails/Id
public IEnumerable<EmpDetail> Get(string Id)
{
    using (WebAPIEntities WE = new WebAPIEntities())
    {
        return WE.TrxDetails.FirstOrDefault(E => E.EmpId == Id);
    }
}