The fact that your child has drifted away from obedience to Allah, may He be exalted, and has chosen for him/herself the path of deviation, misguidance and atheism, should not make you feel anxious or guilty, or feel that the way in which you brought up your children was the cause of that. So do not pay any attention to the whispers of the Shaytaan and do not let the guilt bar you from continuing in your efforts to give your children a good Islamic upbringing and to remain committed and adhering to Islamic teachings.
It is advised that you do not label your child as atheist even if they claim it. He/She might be just in phase of searching because they have doubts like many teenagers do and cannot settle on who they want to be so they call themselves atheists.
If you believe your child has turned atheist or is leaning towards atheism, then engage him/her, talk to him/her and address his/her concerns/doubts about Islam. As a parent, talk to him/her openly without getting frustrated or angry because that will not solve anything. You getting angry with your child will accomplish nothing except to drive you further apart and may damage your relationship forever.
You might want to listen to what he/she thinks. Acknowledge his/her concerns. Make him/her feel loved. This phase is extremely hard for him/her and might cause him/her to become depressed, distant or even suicidal so he/she needs all the support possible.
You should always pray that this is just a phase and they will eventually come back. He/she might be upset with certain cultural or traditional practices that have nothing to do with Islam. Perhaps he/she is being influenced by someone else. Maybe he/she is simply trying to fit in with a new group of atheists whom he/she admires. Perhaps he/she independently came to this conclusion based on his or her own logic but will soon enough find atheism itself is not answering their questions/doubts and they end up not being content with it either.
If in spite of all your efforts, he/she decides to remain atheist, you have no option but to continue to pray that he/she be guided. So turn to your Allah, may He be exalted, and offer a great deal of supplication (du‘aa’) to Him before dawn and when prostrating, in the hope that Allah, may He be exalted, may answer your prayers.
It was narrated that Abu Hurayrah said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “There are three prayers that will undoubtedly be answered: the prayer of one who has been wronged; the prayer of the traveller; and the prayer of a father concerning his child.”
Narrated by at-Tirmidhi (1905), Abu Dawood (1563), and Ibn Maajah (3862)
Allah, may He be exalted, says (interpretation of the meaning):
“Not upon you (Muhammad (blessings and peace of Allah be upon him)) is their guidance, but Allah guides whom He wills” [al-Baqarah 2:272]
“Verily! You (O Muhammad (blessings and peace of Allah be upon him)) guide not whom you like, but Allah guides whom He wills. And He knows best those who are the guided”
If your child starts publicly advocating for atheism and renouncing Islam, this will reflect a sign of genuine clear apostasy. In this obvious case, if he/she dies on such state, he/she will be deprived from all Islamic funeral rights and inheritance.
And Allah knows best.