Do chromosomes swap genetic material in mitosis or meiosis

Meiosis, the sister chromotids match up together and swap legs (sometimes)

The answer is the process of Meiosis. In fact, it occurs in the first part of Meiosis wherein the cell division process divides the chromosome number into two and the swapping of the genetic material of two different parent cells will create a new set of chromosomes through crossing-over. These are parent homologous chromosomes which pair up and recombine in order for the DNA to be arranged and repaired. This programmed procedure creates a brand new DNA for the offspring.