How to maintain a fork of an evolving project while local changes are minimal and mostly related to making project work in personal platform

So I have this exact need:

There is an upstream project doing their own thing over git and I want to build container images locally and commit them to my image repository all while following the same version system as upstream.

To be more precise (perhaps abstract) about my need, what is the best way to apply the same patch when upstream release a new version.

Any input and best practices or lessons learned are welcome.