Carol, Males inherit their Y chromosome from their fathers; that is
why this test is helpful for trancing the paternal line. Therefore,
your son's Y chromosome was inherited from his father, so will not be
helpful in tracing your paternal line, Similarly, as your nephews are
presumably the children of your sisters, they also inherited their
Y-chromosomes from their fathers.
If your father had brothers who had sons, these male first cousins (on
your paternal side) would be candidates for Y testing.
However, a Y-chromosome test alone will not allow you to identify
potential half-siblings, but in combination with an autosomal DNA test
would be helpful.