Is it permissible to divorce a wife suffering from schizophrenia, especially when there is a young daughter, and what are the implications of such a divorce regarding the daughter, the maintenance (nafaqah), and the deferred dowry (mu'akhar), and would divorcing her be considered a sin?

The husband is advised to be patient with his wife's illness and to seek treatment for her, and he will be rewarded for that. If he divorces her, there is no sin upon him, but patience is more commendable.

As for maintenance (nafaqah), it is obligatory upon him and her illness does not negate it. If the illness was insanity prior to the marriage contract, and the husband was unaware of it or did not consent to it after becoming aware, the marriage can be annulled. However, if he was aware of it and consented to it, or found pleasure in her despite it, then he only has the options of divorce or retention, and she is entitled to her agreed-upon mahr (dowry). The mahr is established for her upon consummation of the marriage, and the husband can seek its return from whoever deceived him. Some scholars do not believe in seeking its return from the guardian if the husband has consummated the marriage with her.

Custody (hadhanah) belongs to the mother, subject to certain conditions. If these conditions are not met, custody transfers to the next eligible person. In countries that do not rule by Islamic law, Muslims should choose people of knowledge and righteousness to arbitrate between them in such matters.