What is the ruling of the Sharia regarding a suspicious husband who pronounces divorce repeatedly and claimed that his wife is no longer under his responsibility, knowing that she is committed and denies his accusations of betrayal, and they have three children?

The husband's statement: "You are out of my responsibility" is an ambiguous phrase that could imply divorce or something else. If the husband intended divorce by it, then it has occurred. If he had previously divorced her twice, then she is irrevocably divorced from him (baynunah kubra). However, if he did not intend divorce by it, then no divorce has occurred.