These are those who were either ministering with Paul or ministering to Paul. Alternate translation "The fellow believers."
## especially those of Caesar’s household ##
These are servants who worked in Caesar's palace. This could be translated as "especially the fellow believers who work in the palace of Caesar" (UDB).
## with your spirit ##
Paul refers to the believers by using the word "spirit" which is what enables humans to relate to God. This can be translated as "with you." (See: [[rc://en/ta/man/translate/figs-synecdoche]])