Satan has a number of children which help him and almost all of his children have chosen the same path as he has and thus have been cursed and rejected as well, except for a few of them; like one who lived during the time of the Grand Messenger Hazrat Muhammad (Peace be upon him) and through him embraced Islam.
Just like human beings Satan also has offspring. This has been pointed out in the Quran and in narrations from the Ahlul-Bait (P.B.U.T.). "When We said to the angels, 'Prostrate before Adam,' they prostrated, but not Iblis. He was one of the jinn, so he transgressed against his Lord's command. Will you then take him and his offspring for guardians in My stead, though they are your enemies? How evil is a substitute for the wrongdoers!"
In Allameh Majlisi's book, "The Heavens and the Earth", which is one of the volumes of Baharul Anwar, he states: There is a hadith where Allah says to Iblis "I will give no child to Adam unless I give one like him to you, and every human has a 'twin' satan like itself." Goal of Satan's children in this world, is just like Satan's own goal to misguide mankind, so surely cursing Satan also means cursing his offspring as well. Of course, nearly all of Satan's offspring are such, with the exception of a select few which have become Muslim. In this same book from Allameh Majlisi it states: The Messenger of Allah (Peace be upon him) was asked, "Do you have offspring of Satan from amongst you?" He replied, "Yes, yet God has helped me to make him Muslim"
In closing there are a couple of noteworthy points to keep in mind:
- From the Holy Quran it is gathered that Satan's offspring and tribe's guardianship (or authority) that is mentioned in the Quran is of little significance. For example; perhaps one of them may have [some] influence and or authority upon certain persons but not others, or upon certain actions and not others, or they have no actual authority at all rather their authority is delimited to helping and assisting the main Satan (Iblis) and he is the root of all evil deeds that mankind may do.
- The main Satan (Iblis) was from the jinn, and since in one place in the Quran it has been mentioned that Satan has offspring and in another place it has attributed death and demise to them, then it becomes obvious that jinns also have reproduction, because the precondition of every living organism which has offspring and death is that it can reproduce. Of course the question which will remain unanswered (as it has not been mentioned in the Quran) is whether or not the reproduction of jinns is like that of other creatures via intercourse or by another means?
Sura Kahf – Ayah 50: …Will you then take him and his offspring for guardians in My stead…
Translation of "The Heavens and the Earth" – Pg.243
Translation of "The Heavens and the Earth" – Pg.254
Sura Kahf – Ayah 50
 Sura A'araf – Ayah 27: …Indeed he sees you – he and his hosts – whence you do not see them. We have indeed made the devils friends of those who have no faith.
 Translation of Al-Mizan – Vol.12, Pg.63
 Sura Kahf – Ayah 50: … they prostrated, but not Iblis. He was one of the jinn…
 Sura Kahf – Ayah 50
Sura Ahqaf – Ayah 18: …that have passed away before them of jinn and humans.
Translation of Al-Mizan – Vol.12, Pg.226