Crossing over that results in genetic recombination in higher organisms occurs between :-

During prophase I of meiosis (zygotene), homologous chromosomes pair to form bivalents (tetrads). Each bivalent has four chromatids.
In pachytene, crossing over takes place: segments are exchanged between non-sister chromatids of the homologous chromosomes, with the help of the enzyme recombinase. Chiasmata are the visible points of exchange.
Because the non-sister chromatids come from different parents, this exchange creates new combinations of alleles (genetic recombination).
Exchange between sister chromatids would not produce recombination, because they are identical copies.
So crossing over occurs between non-sister chromatids of a bivalent.