The answer is prophase of meiosis I.
Meiosis is a reducing cell division during which the number of chromosomes is reduced by half in the daughter cells. It consists of meiosis I and meiosis II. Major gene reshuffling takes place during meiosis I. This exchange of genetic material between homologous chromosomes is known as the crossover. Homologous chromosomes are present only in the meiosis I. They pair up during prophase of meiosis I. When they are paired up during prophase I, it is obviously that gene reshuffling takes place during prophase I.