Your father's sister is your aunt. Her brother-in-law is either the brother of her husband or the husband of her sister.
If you are talking about your aunt's brother-in-law's son, the English language has no terms for a relationship between you and him. We would say he is not related to you.
If you are talking about the son of the husband of your aunt's sister, since your aunt's sister is also your father's sister, and her husband's son is her son, the son is your first cousin. If the son is the result of a previous marriage, then he is not related to you unless your aunt formally adopted him, in which case he would be your first cousin.
Your father's nephew is your cousin. That person's son is also your cousin, specifically your first cousin once removed.
you call them your cousin.
Nephew
your nephews
Your cousin.
cousin
cousin!
King
That would be your Cousin.
Your father's brother's son is your first cousin and your daughter's second cousin.
Great nephew
3rd cousin
Nephews
Some would call your nephew's children your grand nephews and grand nieces, others would call then your great nephews and great nieces.
Your father's sister is your aunt. Her son is your first cousin. Her grandson is your first cousin, once removed.