Recombinant chromosomes have a mix of paternal and maternal alleles due to

Crossing over

Explanation:

At Late Prophase  I of meiosis homologous chromosomes  are pair by synapsis, and lie side by side to form a bivalent.

Genetic components present in each homologue crossed to the other at the point of contacts of the arms of chromosomes(chiasmata) with each other. The arms or parts of the chromatids may break and rejoined with  the other chromatids, aiding mix up. The point of the exchange of genetic material is called chiasma. plura chiasmata,

Therefore  genetic materials from  the two bivalent pair get  exchanged or mixed with one another. This is called crossing over. And it forms the basis of chromosomes recombination because assuming the sister chromatids (bivalent)were from fathers and mothers, the exchange of genetic materials ensures chromosomes shuffles which gives rooms for variation