As I understand the world, it's basically women can use magic and men can't. How can men still be useful? Ideas follow:
Let's think about some real world teams. For examples snipers work with a shooter and a spotter. The witch is the shooter, but the man acts as the spotter. He can't cast the spell but he acts as the human equivalent of a targeting computer and is thus critical to delivering fireballs and lightening bolts to their targets.
Another example is craftsman. The men can't wield magic, but can learn enough nonmagical skills to be essential to rituals or runes.
There is the classic D&D example where the female is the physically weak magic user and the man is the meat shield (fighter or paladin class) to keep the witch from getting killed.
Another idea, men have counter magic. Witches have magic, but only men can use counterspells or cast defense shields. They may have to draw on the witch's power to pull this off, but it would make the presence of men in combat critical. Maybe rituals attract the attention of demons or ghosts and only men can create shields to cloak the ritual for hostile entities.
Magic makes men awesome
The average Joe is basically useless. But when a witch pumps magic into him, he gets new abilities. Sky's the limit here - super strength, precognition, healing, illusions, whatever. The key is that only men can do this, but only when empowered by a witch.
Men as mana batteries. Men can gather and/or store crazy amounts of mana, which can then be transferred to the witch for use in spells.
Men soak magic backlash. Witches keep men around to soak negative effects of magic. Depending on how dark you want your story to be, this could lead to death and disfigurement easily.
Men as spell components. Men are needed to perform spells. How they contribute exactly is up to you. Just standing around looking cool? Meditation and concentration? Blood or physical matter needed? Sex magic? Straight up human sacrifice for every high level spell?
Women are not creative. Women are basically really good technicians. They learn and execute magic without issue. But for some reason, they can't creatively think about or interpret magic. Only men can do that. Which means that men must study magic, understand it, train the witches, and are the only source of new spells in the world. Lots of questions about why this is so - maybe some ancient god purposely separated these two things. Or it's the result of a disastrous worldwide magic accident.
Only men can do one of the three types of magic. Self explanatory, some type of magic is completely closed off to women.
Lock and key. Men release the restraints on women so they can use magic. Maybe this has to happen every time, every x years, or just once in a witches life. Might require physical contact or some kind of ritual, or something else (marriage?, human sacrifice?). The man should get something from doing this, like money or immunity to the witches magic. Maybe the inner strength of the man dictates how much power the witch can use. So there are men capable of releasing incredibly powerful witches and they are in high demand.