Meyers gazetteer shows 9 places in Germany named Neuhütten; by your family tree you want the one in Bavaria. Meyers gazetteer says Neuhütten in Bavaria has one Catholic Church (Bavaria is predominantly Catholic). The church records would be your best resource.
FamilySearch, unfortunately, does not have records for this parish.
There are some German Catholic Church records at Matricula (this is a work in progress), which are organized by diocese. I think Neuhütten is in the Diocese of Passau Augsburg; this comes from comparing a map of Bavarian dioceses with a map showing where Neuhütten is. Unfortunately, I did not find this town in the list of parishes in the Diocese of Passau Augsburg.
If you have a definitive diocese for Neuhütten, take another look at Matricula, or check periodically in the future as resources are expanding there. The website is in German and English, is free, and relatively easy to use. There is no overall index of names to search, although some volumes of church records have contemporary indices. See https://www.icar-us.eu/en/cooperation/online-portals/matricula/
Neuhütten seems to be rather small today. It is possible the church there was a branch of another church in a nearby larger town.
Best of luck.
edited …
Changed Passau to Augsburg … still did not find it.