Organ belonging to me? That's not true (2,3)
I believe the answer is:
my eye
'that's not true' is the definition.
('my eye' is an expression of disbelief)
'organ belonging to me?' is the wordplay.
I cannot really see how this works, but
'organ' could be 'eye' (eye is a kind of organ) and 'eye' is found in the answer.
The remaining letters 'my' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for my eye that I've seen before include "I notice things catching this" , "Bull" , "Certainly not" , "Nonsense! (slang)" , "Interjection expressing disagreement" .)