Roman Emperors

Caesar	46 BC ‑ 44	Jesus born
Augustus	44 ‑ 14 AD	Jesus born
Tiberius	14 ‑ 37	Jesus crucified
Caligula	37 ‑ 41
Claudius	41 ‑ 54	Paul requests trial
Nero	54 ‑ 68	Paul executed
(several)	68‑69	Jewish War started
Vespasian	69 ‑ 79	Jewish War ended

Note: Augustus did not have full power until after the Battle of Philippi in 42 BC (conspirators Cassius and Brutus defeated) and then after 31 BC (Mark Antony and Cleopatra defeated).

Acts 25:21 But when Paul had appealed to be reserved unto the hearing of Augustus, I commanded him to be kept till I might send him to Caesar. [kjv]

του δε παυλου επικαλεσαμενου τηρηθηναι αυτον εις την του σεβαστου διαγνωσιν εκελευσα τηρεισθαι αυτον εως ου αναπεμψω αυτον προς καισαρα [gnt]

Here «διαγωςσιν» is "hearing".

Note that the Vulgate "Augusti" and King James "Augustus" refer to Emperor at the birth of Jesus. The Greek, however, does not have this word - but it might be inferred from the word «σεβαστου» for "respected". The Luther German has "Kaisers" for "Caesar" which is the origin of the German word "Kaiser".

All versions have "Caesar" at the end of the verse.

The ancient Greek word "Καῖσαρ" ≈ "Caesar" from the Latin word "Caesar" ≈ "Caesar".
The modern Greek word "Καίσαρας" (KEH-sa-ras) ≈ "Caesar".
The modern Greek word "Αύγουστος" (AEE-gu-stos) ≈ "Augustus".
The modern Greek word "σεβαστή" (seh-vas-TEE) ≈ "respected".

Sevastopol: Late 18th century. From Ukrainian Севасто́поль (Sevastópolʹ) and Russian Севасто́поль (Sevastópolʹ), from Ancient Greek Σεβαστόπολις (Sebastópolis) from σεβαστός (sebastós, “august”) + πόλις (pólis, “city”), probably after Empress (=Augusta) Catherine II of Russia. Wiktionary: 2022-12-15

Acts 25:21

All

KJV: But when Paul had appealed to be reserved unto the hearing of Augustus, I commanded him to be kept till I might send him to Caesar.

Greek: του δε παυλου επικαλεσαμενου τηρηθηναι αυτον εις την του σεβαστου διαγνωσιν εκελευσα τηρεισθαι αυτον εως ου πεμψω αναπεμψω αυτον προς καισαρα

Latin: Paulo autem appellante ut servaretur ad Augusti cognitionem iussi servari eum donec mittam eum ad Caesarem

Luther: Da aber Paulus sich berief, daß er auf des Kaisers Erkenntnis behalten würde, hieß ich ihn behalten, bis daß ich ihn zum Kaiser sende.

... more to be added ...