Making my own special type of variable

edit

You can't solve your problem by subclassing Expression, this requires you to assign data to every expression. Whats the data associated to the Expression a+b?

Since you only want to associate something to variables, you can just use a dictionary:

sage: var('a, b')
(a, b)
mydata = { a:'foo', b:'bar' }
sage: p = ((a + b)^2).expand()
a^2 + 2*a*b + b^2
sage: p.operands()[0].operands()[0]
a
sage: mydata[_]
'foo'

This is not a complete answer, but here are some useful methods of the symbolic ring and elements for retrieving wrapped python objects:

sage: a=SR(Mod(8,3))
sage: a
2
sage: type(a)
<type 'sage.symbolic.expression.Expression'>
sage: type(a.pyobject())
<type 'sage.rings.finite_rings.integer_mod.IntegerMod_int'>
sage: b=SR._force_pyobject('test')
sage: b
'test'
sage: type(b)
<type 'sage.symbolic.expression.Expression'>
sage: type(b.pyobject())
<type 'str'>