The Smashing Pumpkins singer shares a love/hate relationship with the Hole frontwoman and has launched a tirade against her for apparently using songs he wrote on her new album 'Nobody's Daughter'.
Billy - who is credited as co-writer of four tracks on the album - wrote on his twitter feed: "My face is my face, my heart is my heart, my money is my money. Oh, and my songs are MY songs.
"If you can't write your own songs maybe you should just be happy that you fooled someone into doing your work for you."
Billy - who at one time was romantically linked to Courtney - then started to get personal and suggested Courtney should live off the fortune of her late husband, Nirvana singer Kurt Cobain, rather than pursue her music career.
He added: "Or maybe you should go somewhere nice and live off your husband's money, u know the money he made for writing all those great songs (sic)."
He also blasted Courtney for not looking after her daughter with Kurt - 17-year-old Frances Bean - whom she was legally separated from last year when she went to live with her grandmother and Kurt's sister and applied for a restraining order against Courtney.
He added: "The world is aware of your lack of responsibility, as seen in the gov't taking away your parental right (sic).
"Only u could abandon such a beautiful, incredible child who is smarter than u, cooler than u, and better than u. Oops, did I say too much (sic)?"
In an uncharacteristically short and restrained response, Courtney wrote: "All I am is nice about you so if you wanna be mean, be mean."