This is a metaphor that means to accuse someone in court. Alternate translation: "spoke to me against this man" (See: [[rc://en/ta/man/translate/figs-metaphor]])
The abstract nouns "sentence" and "condemnation" can be expressed as verbs. The phrase "a sentence of condemnation" implies that they were requesting that Paul be executed. Alternate translation: "they asked me to sentence him to death" or "they asked me to condemn him to death" (See: [[rc://en/ta/man/translate/figs-abstractnouns]] and [[rc://en/ta/man/translate/figs-explicit]])