Will the husband be sinful if he does not deny the paternity of his wife's child from adultery by way of li'an, even though he knows of her adultery, if the purpose of not performing li'an is to conceal her and to avoid certain harms, especially since the wife has shown repentance and remorse?

The wife's confession of adultery does not necessitate the husband's repudiation of his child through li'an (oath of condemnation). Rather, this is required only if the husband is certain that the child is not his. However, if there is a possibility that the child is from the husband, he is not obliged to repudiate him, for the default is that the child belongs to the marriage bed. But if the husband is certain that the child is not his, he must repudiate him through li'an to avoid the harms resulting from it. A condition for repudiating the child through li'an is that the husband has not acknowledged his lineage or remained silent about repudiating him for a long period. If the husband has acknowledged the lineage or remained silent about the repudiation, then he has no right to li'an.