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Illegal alien, I guess. It seems that when he left his missus, he lost his right to live and work in Switzerland.
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This. If you are in the country through marriage, and then give the authorities reason to believe this marriage isn't valid, like by having a baby with someone else, you lose your permit. But the permit must have lapsed a bit prior to get the arrest and the ban- you wouldn't get arrested and banned based on a phone call from a European spouse saying you left, unless you had been gone like four years. If you are married to a European, unless mixed Swiss couples, you don't have to live together to keep the permit. So there is more to this story- most likely a longer timeline.
OP, you could try to appeal the ban- you can waste a lot of money (10k CHF or more) on lawyers but success rates are not high- but what you can do in the meantime is prove to the Swiss authorities that you have a close relationship with your child. It's probably not old enough to talk on the phone, but you need to start making proof now and keeping it safe that you are involved in the kid's life: phone records, send whatever money you can, letters, emails, etc. Then it will be easier for you to visit when the ban is lifted. If you don't prove constant contact with your child (or the baby mama if the child is young), the Swiss even refuse tourist visas for parents. The Swiss also only rarely give right to residence to parents of Swiss children, and this only when there is proof of an extremely close relationship.