deisidaimonia refers to the religious matter that was the subject of disputes in Acts 25:19.

The attested use concerns a religious matter: in Acts 25:19, the genitive singular noun occurs in disputes described as being about the parties' own religion.

1. A religious matter under dispute · dominant

   In Acts 25:19, the genitive singular form occurs in the description of disputes concerning the parties' own religious matter; the APB renders the clause, "Instead they had certain disputes with him about their own religion."

   Acts 25:19

In the Anselm Project Bible: In Acts 25:19, the APB presents the disputed subject as "their own religion." This rendering confirms the clause's overall subject rather than isolating every feature of the Greek noun.