Is a child considered illegitimate if born of intercourse during the waiting period (iddah) without the intention of reconciliation, following an irrevocable divorce due to a civil marriage that was later discovered to be invalid?

If a civil marriage takes place without a guardian or witnesses, but with public declaration and the absence of any legal impediments, and it results in the effects of a valid marriage, such as establishing paternity, especially if the couple believes in its validity, then it must be renewed to fulfill the legal conditions and pillars. If a man has intercourse with his wife during her waiting period (iddah) without the intention of reconciliation, this is considered intercourse by شبهة (doubt/semblance) and not zina (fornication/adultery). The child resulting from it is legitimate and not an illegitimate child. The saying that the child of zina is in Hell is false and contrary to Islamic law, as "no bearer of burdens will bear the burden of another."