Enumerable.Concat not working

That is because Concat will return a new instance of your enumerable.

Either use in your else :

tst = tst.Concat(...)

Or Change your Enumerable into list from the beginning :

string[] values = Acode.Split(',');
List<Test> tst= new List<Test>;

foreach (string a in values)
{
    tst.AddRange(entities.Test.Where(g => (g.TCode == Convert.ToInt16(a))));
}

return tst;

Concat doesn't modify anything - it returns a new sequence, which you're currently ignoring.

However, rather than using Concat, you should just use SelectMany to flatten the sequence:

string[] values = Acode.Split(',');
return values.SelectMany(a => entities.Test.Where(t => t.TCode == Convert.ToInt16(a)))
             .ToList();

Or more efficiently, convert values into a List<short> and then you can do one query:

List<short> values = Acode.Split(',').Select(x => short.Parse(x)).ToList();
return entities.Test.Where(t => values.Contains(t.TCode)).ToList();