What is the ruling on a husband who refuses divorce, abstains from financially supporting his children, and denies their lineage after his wife requests divorce due to his bad character and companionship?

If a man says, "They are not my children and I do not want them," intending to deny their lineage, then this is a grave transgression and an accusation that necessitates legal punishment (hadd) or a mutual imprecation (li'an), based on the Prophet's (peace be upon him) saying: "Any man who denies his child while looking at him, Allah will veil Himself from him and expose him before all people, past and present."

However, if he means that they are not attached to him, then such a statement is inappropriate for him to make. It does not permit him to abandon his wife and children or neglect their financial support. He is sinful for his dereliction, as the Prophet (peace be upon him) said: "It is sufficient sin for a man to neglect those whom he supports." He must fulfill the rights of his wife and children, and his wife has the right to take him to court if he fails to do so.