If I divorce my wife, and years later she claims to have conceived from me and gives birth, is the child legally mine, does he inherit from me, and am I legally responsible for him?

Scholars have differed regarding the child's attribution to you. The majority (Hanafi, Hanbali, and Shafi'i schools) hold that the child is not attributed to you, while the Maliki school holds that the child is attributed to you if she gives birth to him within five years. The latter opinion is the preponderant one.