Christians believe that Jesus Christ was the son of god (Allah). Islam follows from both Judaism and Christianity, building upon them, absorbing Jesus into the Quran, but not his divinity. So when the question comes up — did Allah have a son? — the answer is no. But that leaves open the question, Could Allah have a son?
Here the Quran is uncertain. First in verse 39:4 he could have had a son had he chosen to. For whatever reason he chose not to. But then we look back to verse 6:101 and we find that Allah could not have had a son because he was a permanent bachelor. Apparently, in order for the Almighty, Creator of Everything to father a child, he needs a woman. And honestly, who among you would desire that the father of your children to be a genocidal maniac? Then again, even Hitler got married.
Unfortunately, the Quran does not even bother to ask if Allah could have a daughter.