One of my ancestral surnames is Ziesenis and I'd like to know what it means. They were Prussian immigrants to the US back in the 1800s.
We definitely can't give you concise directions on the genealogy of German surnames within the scope of this site dedicated to language.
Nevertheless some hints on the language aspect of this name may help:
Ziese f. / Ziesen pl. This used to be a name for taxes in Preussia, similar to the sales taxes today. It is unclear as to why the suffix -(n)is was added, but from common understanding of this suffix in other nouns it may have had a meaning roughly like "who was attached to taxes".
Ziese f. This is a name of a small stream in the north-east of Germany. As names often come from locations we can speculate that somebody added a latinising suffix -nis to indicate "of origin near the Ziese".