I don’t have/haven’t got children. are both correct. You can also say “I have no children.”

"I don't have any children" is the better option here. "I haven't children" and similar uses of "haven't" were used pretty common in older English, so you might come across that grammar construction in old novels, period movies, etc, but nowadays the best option is definitely "I don't have children."

Hi Gilliard, the first sentence is correct you can say I don't have children or I haven't got any children.

Hello Gilliard: I don't have any children. If you plan in the future to have children you can say I don't have children yet. If you are looking to improve formating sentence structures my classes are open for new enrollments starting today. Please look at my profile, reviews and schedule. I offer trial classes as well. See you this week.

I don't have children is quite better.