Practically: there's almost no chance this will cause you issues. If you're worried, take a train to a nearby airport outside of Switzerland (eg Milan/Lyon/Stuttgart) and fly from there. If you're flying to Portugal then you won't go through passport control; if you're flying to the UK then you w...
"On the basis of a Portuguese residence permit you can stay in Switzerland for up to 90 days as long as the Portuguese residence permit remains valid": a citizen of the UK does not require a valid Schengen residence permit (nor visa, etc.), to stay in Switzerland for 90 days in a 180-day period.
As a note for non-EU-residents: Absolutely do not go outside Switzerland inside Schengen if you're overstaying, instead fly directly out. If found out you will be charged not just with overstaying but illegal border crossing, a situation I observed happen exactly as described (overstayed in Switzerland, came to Munich to fly) when doing translation at the border. This is a much worse outcome for you.
@GiacomoCatenazzi to be clear(er): the 90 day limit applies to all Schengen countries collectively other than Portugal while the Portuguese residence permit is valid, and to the entire Schengen area if it is not valid, though I suspect that Swiss law has nothing to say about, e.g., a Portuguese resident who arrives in Switzerland after spending 91 days in Spain. Technically, that person is "sans papiers" at the moment of arrival, but practically speaking there's no enforcement.
@MJeffryes do those checks extend to database searches or are they like other internal controls I've experienced, where a passport and Portuguese residence permit would be enough?
@ave Is that really much worse? Or simply something the German police had to rely on because the overstay is none of their concern and not something they could act on?
@Relaxed the people got charged for both overstaying a schengen visa and for illegal border crossing, so clearly overstay is their concern too. I would also suspect it's easier to argue "I'm 70, I came to visit my son after his marriage, I was looking at the validity range, not the 72 days of validity" when getting a new visa if one does not also have a charge for illegal border crossing that they (were effictively forced to) sign an admission for.
@ave The German police charged them for overstaying even though they were caught on entry? That's odd… But either way it's true that crossing the border invites scrutiny. I am not convinced it makes a huge difference for a subsequent application either. It's not really relevant to the OP though, they have a residence permit and they are British so they will never have to apply for a Schengen visa.
@Relaxed No. This was at the airport passport control as they were on their eay to their flight out of schengen. Passport police initiated the action. They were told that they must sign the doc agreeing to their crimes to continue and give their address, else they'd be pulled into another room and can get a lawyer (they'd get a call with consulate also), but the police told them they'd miss their flights in this case. + Even a day of overstay can make a huge difference for a subsequent application, in this case they may receive an entry ban, which would also affect non-visa-nationals equally.
@phoog They have a booth setup that looks much like the ones at airports so I assume they have access to the same IT system that would check whatever databases they have access to at the airport. At least as I recall
@ave So they didn't even have any direct evidence of this alleged irregular border crossing and they tried to pressure these people into admitting it? How long was this overstay? Since they are dealing with it at the airport, I assume we are talking about people who did not have a residence permit. All this seems rather unusual and very far from the OP's situation.
Beyond that, a single day is very unlikely to result in a ban but a past overstay can certainly call your intents and reliability into question, that's why I am not buying that crossing the border makes a huge difference on top of that. Note that issuing a ban directly is not possible for a residence permit holder, instead the German police would have to ask Portugal to rescind the residence permit, whose continued validity is a real issue in this case as the answer rightfully points out.
@Relaxed "the German police had to rely on because the overstay is none of their concern" Overstays is definitely of concern for the German Police, what grounds do you have to say the German Police does not deal with overstays? They have a duty according to the German Residence Act Sec 87.
@Dr.Snoopy What I had in mind is an overstay in Switzerland for someone with a residence permit from another EU country (because at that point the person hasn't overstayed in Germany, overstays in the Schengen area as whole is not relevant / meaningful, and evidence that they have overstayed at all would be weak). I obviously didn't mean that the German police never ever cares about overstays of any kind.
@Relaxed Seems it was someone overstaying in Switzerland that was caught in Germany, the German Police would have to report that anyway, independent of any visas or residence permits. The procedure would be different but reporting will happen anyway. And if it was at an airport, it was more likely the German Federal Police. If they are overstaying in Schengen, they are also overstaying in Germany, assuming they have a non-German residence permit/visa.
@Dr.Snoopy Apparently the case ave had in mind did not involve a residence permit and we got into this long side discussion that has very little to do with the OP's situation. The main difference is that if you catch someone with a visa and an entry stamp more than 90 days in the past, that's all the evidence you need and you can do anything including cancelling the visa or issuing a ban. If you catch someone with a residence permit, it's a lot more complicated to establish exactly what rules has been breached (if at all) and there isn't much you can do beyond a fine and notifying Portugal.
@Relaxed Surely its more complicated but not impossible, I have entry/exit stamps in my passport and I have a residence permit, its inconsistent but the information can be right there, and there are other ways.
@Dr.Snoopy No, the stamps are not in question and the EES doesn't really matter to this, the problem is that you need to establish that the person did not move back and forth between their country of residence and the rest of the Schengen area, which still will not be tracked by the EES. As I wrote in my answer, I still think that repeated entries and exits from outside the Schengen area to the same country ought to be suspicious but in most cases it's a mess and something the police doesn't bother investigating.
That's why I was interested in understanding exactly what happened in ave's example as it seemed unusual (as is bothering with illegal border crossing when you have an open-and-shut case of overstay, for the same burden-of-proof reasons).
Sure, it could be just as simple as the person revealing that information in the exit interview to the German Border Police, saying they stayed 100 days in Switzerland, for example.
Discussion on answer by Edd: I overst…
Discussion on answer by Edd: I overst…