A nucleus within an ascus undergoes meiosis, producing four haploid spores, which then undergo mitosis, producing eight haploid ascospores. These haploid ascospores contain a maximum of different genetic types.

Four.

Explanation:

Initially four haploid spores are produced by meiosis. We know that during meiosis pairing between homologous chromosomes occurs and this created genetic difference between the divided cells. Exchange of genetic material doesn't occur during mitosis so mitotically divided cells are similar. Thus when spores divide by mitosis and become eight in number, here will be no new genetic difference.

The complete sentence will be -

A nucleus within an ascus undergoes meiosis, producing four haploid spores, which then undergo mitosis, producing eight haploid ascospores. These haploid ascospores contain a maximum of four different genetic types.