Can a non-disjunction event occur in meiosis II (in the paternal gametes) to result in an XXY male?
The reason maternal non-disjunction during meiosis II can produce XXY offspring.


In this case, meiosis I occurs as normal so that after the first division the replicated homologous chromosomes, each consisting of two chromatids connected at a centromere, have separated. If a non-disjunction occurs at this point, haploid cells will not be formed. Instead, the sister chromatids of a replicated chromosome will not be separated and a gamete containing two X chromosomes will be formed. When this gamete combines with a sperm containing a Y chromosome, the offspring has the XXY genotype.


The reason paternal non-disjunction during meisosis II cannot produce XXY offspring. 


This is similar to the maternal case except that after meiosis I, in one cell will be two YY chromosomes while the other cell will be two XX chromosomes. When non-disjunction occurs (assuming it occurs in both divisions), these chromosome arrangements remain the same and two cells are formed. One with two XX chromosomes and one with two YY chromosomes. If either of these gametes combines with a female X gamete, either XYY or XXX will be formed but never XXY.