mitosis: It depends on what kind of cell it is. If it is a somatic (body cell) then it will have the same materials and everything as the parent cell.
meiosis: But if it is a gamete cells then it requires the fusion of two different 'cells' and they combine crossing over-the chromosomes from the different people combine together to get different combinations and the new cells are haploid (half the amount of chromosomes) so the new cell will have both genetic material from both parents-paternal and maternal.