Which part of the plant or flower contributes in the form of false fruit like apple?

A false fruit (pseudocarp) is a fruit in which the fleshy edible part develops not from the ovary but from some other floral part. In apple (and pear), the fleshy edible portion develops from the thalamus (receptacle) which grows around the true fruit (the core). The ovary forms only the central core enclosing the seeds. Hence the thalamus is the floral part responsible for the false-fruit nature of an apple.