I think solution 1 got the wrong end of the stick. Based on your comment you just need to add and AND clause to your query (and as pointed out by Slacker007, correct your column list). E.g.
Select ID, Name, Designation, Level, userid
from EmployeeList where level like '00010104%'
and Designation like 'AE%'
If you also want to include the "sub-child" designation you mention then add an OR clause but you will need to enclose it in brackets e.g.
Select ID, Name, Designation, Level, userid
from EmployeeList where level like '00010104%'
and ( Designation like 'AE%' or Designation like 'JE%' )