Duties and rights of the “city police”?

Hello, after the football match yesterday evening I noticed that in the whole city center traffic is regulated by the “city police” that has been in existence for some time. But what exactly is that? Are it the same ones that formerly had “order office” on the vehicles, or is this a completely independent group? Does it belong to the police or city administration? And above all, what rights do they have? – only traffic monitoring? – can they also carry out traffic controls? – Penitence handing out elde/punishments? Thank you, greeting Martin